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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)- 14:07, 8 December 2021 Caliburn talk contribs created page Horizontal Section preserves Subsets (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be sets. Let $A \subseteq B$ be subsets of $X \times Y$. Let $y \in Y$. Then: :$A^y \subseteq B^y$ where $A^y$ is the $x$-vertical section of $A$ and $B^y$ is the $x$-vertical section of $B$. </onlyinclude> == Proof == Note that if: :$x \in A^y$ from the definition of Definition:Vertical Sectio...")
- 14:05, 8 December 2021 Caliburn talk contribs created page Horizontal Section preserves Increasing Sequences of Sets (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be sets. Let $\sequence {A_n}_{n \mathop \in \N}$ be an increasing sequence in $X \times Y$. Let $y \in Y$. Then: :$\sequence {\paren {A_n}^y}_{n \mathop \in \N}$ is an increasing sequence. </onlyinclude> == Proof == Since $\sequence {A_n}_{n \mathop \in \N}$ is increasing...")
- 14:04, 8 December 2021 Caliburn talk contribs created page Vertical Section preserves Increasing Sequences of Sets (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be sets. Let $\sequence {A_n}_{n \mathop \in \N}$ be an increasing sequence in $X \times Y$. Let $x \in X$. Then: :$\sequence {\paren {A_n}_x}_{n \mathop \in \N}$ is an increasing sequence. </onlyinclude> == Proof == Since $\sequence {A_n}_{n \mathop \in \N}$ is increasing...")
- 14:01, 8 December 2021 Caliburn talk contribs created page Vertical Section preserves Subsets (Created page with "== Theorem == <onlyinclude> Let $X$ and $Y$ be sets. Let $A \subseteq B$ be subsets of $X \times Y$. Let $x \in X$. Then: :$A_x \subseteq B_x$ where $A_x$ is the $x$-vertical section of $A$ and $B_x$ is the $x$-vertical section of $B$. </onlyinclude> == Proof == Note that if: :$y \in A_x$ from the definition of Definition:Vertical Sectio...")
- 13:35, 8 December 2021 Caliburn talk contribs created page Union is Increasing Sequence of Sets (Created page with "== Theorem == <onlyinclude> Let $\sequence {D_n}_{n \mathop \in \N}$ be a sequence of sets. Then: :the sequence $\ds \sequence {\bigcup_{k \mathop = 1}^n D_k}_{n \mathop \in \N}$ is increasing. </onlyinclude> == Proof == We have: :$\ds \bigcup_{k \mathop = 1}^{n + 1} D_k = D_n \cup \bigcup_{k \mathop = 1}^n D_k$ From Set is Subset of Union, we have:...")
- 12:26, 8 December 2021 Caliburn talk contribs created page Definition:Pi-System (Created page with "== Theorem == <onlyinclude> Let $X$ be a set. Let $\Pi \subseteq \map {\mathcal P} X$ be a collection of subsets of $X$. We say that $\Pi$ is a '''$\pi$-system''' {{iff}} it is closed under finite intersection. That is: :for all finite collections $A_1, A_2, \ldots, A_n$ of sets in $\Pi$ we have $\ds \bigcap_{i \mathop = 1}^n A_i \in \P...")
- 07:20, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/87 - Another Street Puzzle (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $87$ == ;Another Street Puzzle <onlyinclude> :''A long street in Brussels has all the odd numbers of the houses on one side and all the even numbers on the other.'' :''$(1)$ If a man lives in an odd-numbered house and all the numbers on one side of him, added together, equal the numbers on the other side,'' :::''how many houses are there, and what is the number of his house?'' :''...")
- 07:07, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/86 - A New Street Puzzle (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $86$ == ;A New Street Puzzle <onlyinclude> :''Brown lived in a street which contained more than twenty houses, but fewer than five hundred,'' ::''all numbered one, two, three, four, etc., throughout.'' :''Brown discovered that all the numbers from one upwards to his own number inclusive summed to exactly half the sum of all the numbers from one up to, and including, the last house...")
- 06:58, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/85 - The House Number (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $85$ == ;The House Number <onlyinclude> :''A man said the house of his friend was in a long street,'' ::''numbered on his side one, two, three, and so on,'' ::''and that all the numbers on one side of him added up exactly the same as all the numbers on the other side of him.'' :''He said he knew there were more than fifty houses on that side of the street,'' ::''but not as many as...")
- 06:26, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/84 - The Three Brothers (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $84$ == ;The Three Brothers <onlyinclude> :''The discussion arose before one of the tribunals as to which of a tradesman's three sons could best be spared for service in the Army.'' :''"All I know as to their capabilities," said the father, "is this:'' ::''Arthur and Benjamin can do a certain quantity of work in eight days,'' ::''which Arthur and Charles will do in nine days,'' ::...")
- 06:20, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/83 - A Critical Vote (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $83$ == ;A Critical Vote <onlyinclude> :''A meeting of a charitable society was held to decide whether the members should expand their operations.'' :''It was arranged that during the count those in favour of the motion should remain standing,'' ::''and those who voted against should sit down.'' :''"Ladies and gentlemen," said the chairman in due course, "I have the pleasure to a...")
- 06:13, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/82 - Army Figures (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $82$ == ;Army Figures <onlyinclude> :''A certain division in an army was composed of a little over twenty thousand men, made up of five brigades.'' :''It was know that one third of the first brigade,'' ::''two-sevenths of the second brigade,'' ::''seven-twelfths of the third,'' ::''nine-thirteenths of the fourth,'' ::''and fifteen-twenty-seconds of the fifth brigades happened in e...")
- 06:07, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/81 - Pussy and the Mouse/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $81$ == ;Pussy and the Mouse {{:Henry Ernest Dudeney/Modern Puzzles/81 - Pussy and the Mouse}} == Solution == Barrel no. $4$. == Proof == :$500 \pmod 8 = 4$ == Sources == * {{BookReference|Modern Puzzles|1926|Henry Ernest Dudeney|prev = Henry Ernest Dudeney/Modern Puzzles/80 - The Flocks of Sheep/Solution|next = Henry Ernest Dudeney/Modern Puzzles/82 - Army Figures/Solution...")
- 06:07, 8 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/81 - Pussy and the Mouse (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $81$ == ;Pussy and the Mouse <onlyinclude> :''"There's a mouse in one of these barrels," said the dog.'' :''"Which barrel?" asked the cat.'' :''"Why, the five hundredth barrel."'' :''"What do you mean, the fiove hundredth? There are only five barrels in all."'' :''"It's the five hundredth if you count backwards and forwards this way."'' :''And the dog explained that if you count l...")
- 23:08, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/80 - The Flocks of Sheep (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $80$ == ;The Flocks of Sheep <onlyinclude> :''Four brothers were comparing the number of sheep that they owned.'' :''It was found that Claude had ten more sheep than Dan.'' :''If Claude gave a quarter of his sheep to Ben,'' ::''then Claude and Adam would together have the same number as Ben and Dan together.'' :''If, then, Adam gave one-third to Ben,'' ::''and Ben gave a quarter o...")
- 23:03, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/79 - Egg Laying (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $79$ == ;Egg Laying :''The following is a new variation of an old friend.'' :''Though it looks rather complicated and difficult, it is absurdly easy if properly attacked.'' <onlyinclude> :''If a hen and a half lays an egg and a half in a day and a half,'' ::''how many and a half who lay better by half will lay half a score and a half in a week and a half?'' </onlyinclude> === H...")
- 22:48, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/78 - The Miller's Toll/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $78$ == ;The Miller's Toll {{:Henry Ernest Dudeney/Modern Puzzles/78 - The Miller's Toll}} == Solution == :$1 \tfrac 1 9$ bushels == Proof == Let $x$ bushels be the total quantity of flour ground. Then: :$x - \dfrac x {10} = 1$ from which: :$x = \dfrac {10} 9$ The result follows. {{qed}} == Sources == * {{BookReference|Modern...")
- 22:45, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/78 - The Miller's Toll (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $78$ == ;The Miller's Toll :''Here is a very simple puzzle, yet I have seen people perplexed by it for a few minutes.'' <onlyinclude> :''A miller was accustomed to take as toll one-tenth of the flour that he ground for his customers.'' :''How much did he grind for a man who had just one bushel after the toll had been taken?'' </onlyinclude> === Henry Ernest Dudeney/Modern Puzzl...")
- 22:14, 7 December 2021 Caliburn talk contribs created page User:Caliburn/s/mt/Signed Measure of Limit of Decreasing Sequence of Measurable Sets (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma}$ be a measurable space. Let $E \in \Sigma$. Let $\sequence {E_n}_{n \mathop \in \N}$ be an decreasing sequence of $\Sigma$-measurable sets such that: :$E_n \downarrow E$ where $E_n \downarrow E$ denotes limit of decreasing sequence of sets, and: :there exi...")
- 22:10, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/Arithmetical and Algebraical Problems/Various Arithmetical and Algebraical Puzzles (Created page with "== {{AuthorRef|Henry Ernest Dudeney}}: {{BookLink|Modern Puzzles|Henry Ernest Dudeney}}: Arithmetical and Algebraical Problems == <onlyinclude> ==== $78$ - The Miller's Toll ==== {{:Henry Ernest Dudeney/Modern Puzzles/78 - The Miller's Toll}} ==== $79$ - Egg Laying ==== {{:Henry Ernest Dudeney/Modern Puzzles/79 - Egg Laying}} ==== Henry Ernest Dudeney/...")
- 21:57, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/77 - The Ten Volumes (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $77$ == ;The Ten Volumes <onlyinclude> :''As an extension of the last puzzle, let us introduce a $10$th volume marked $0$.'' :''If we arrange the $10$ volumes as follows, we get a sum of money correctly multiplied by $2$.'' <pre> 54 3 9 2 108 7 6 </pre> :''Can you do the same thing with the multiplier $4...")
- 21:56, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/77 - The Ten Volumes/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $77$ == ;The Ten Volumes {{:Henry Ernest Dudeney/Modern Puzzles/77 - The Ten Volumes}} == Solution == <pre> 81 6 9 4 --------- 325 7 0 </pre> == Sources == * {{BookReference|Modern Puzzles|1926|Henry Ernest Dudeney|prev = Henry Ernest Dudeney/Modern Puzzles/76 - The Nine Volumes/Solution|next = Henry Ernest Dudeney/Modern Puzzles/78 - The Miller's Toll/Solution...")
- 21:51, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/76 - The Nine Volumes/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $76$ == ;The Nine Volumes {{:Henry Ernest Dudeney/Modern Puzzles/76 - The Nine Volumes}} == Solution == {{AuthorRef|Henry Ernest Dudeney|Dudeney}} offers up $2$ solutions: <pre> 21 8 7 3 -------- 64 5 9 </pre> <pre> 8 5 7 3 -------- 24 16 9 </pre> == Sources == * {{BookReference|Modern Puzzles|1926|Henry Ernest Dudeney|prev = Henry Ernest Dudeney...")
- 21:48, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/76 - The Nine Volumes (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $76$ == ;The Nine Volumes <onlyinclude> :''In a small bookcase were arranged $9$ volumes of some big work,'' ::''numbered from $1$ to $9$ inclusive,'' ::''on $3$ shelves exactly as shown:'' <pre> 26 5 9 7 184 3 </pre> :''The $9$ digits express money value.'' :''You will see that they are so arranged that $\pounds 26 \ 5 \shillings \ 9 \oldpen...")
- 21:31, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/75 - A Teasing Legacy (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $75$ == ;A Teasing Legacy <onlyinclude> :''Professor Rackbrain left his typist what he called a trifle of a legacy if she was able to claim it.'' :''The legacy was the largest amount that she could find in an addition sum,'' ::''where pounds, shillings and pence were all represented and no Definition:...")
- 21:30, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/75 - A Teasing Legacy/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $75$ == ;A Teasing Legacy {{:Henry Ernest Dudeney/Modern Puzzles/75 - A Teasing Legacy}} == Solution == In the words of {{AuthorRef|Henry Ernest Dudeney|Dudeney}}: :''The best answer, as far as I have been able to discover, is the following:'' <pre> £ s. d. 296 - 5 8 - 7 --------- £304 1 - </pre> == Sources == * {{BookReference|Modern Puzzles|1926|Henry Erne...")
- 21:20, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/74 - Queer Division/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $74$ == ;Queer Division {{:Henry Ernest Dudeney/Modern Puzzles/74 - Queer Division}} == Solution == :$35 \, 641 \, 667 \, 749$ == Proof == {{ProofWanted|Probably a technique can be used from the theory of modulo arithmetic}} == Sources == * {{BookReference|Modern Puzzles|1926|Henry Ernest Dudeney|prev = Henry Ernest Dudeney/Modern Puzzles/73 - Alphabetical Arithmetic/Solut...")
- 21:15, 7 December 2021 Caliburn talk contribs created page User:Caliburn/s/mt/Measure of Limit of Decreasing Sequence of Measurable Sets (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma, \mu}$ be a measure space. Let $E \in \Sigma$. Let $\sequence {E_n}_{n \mathop \in \N}$ be an decreasing sequence of $\Sigma$-measurable sets such that: :$E_n \downarrow E$ where $E_n \downarrow E$ denotes limit of decreasing sequence of sets, and: :there exist...")
- 21:15, 7 December 2021 Prime.mover talk contribs created page Henry Ernest Dudeney/Modern Puzzles/73 - Alphabetical Arithmetic/Solution (Created page with "== {{BookLink|Modern Puzzles|Henry Ernest Dudeney}} by {{AuthorRef|Henry Ernest Dudeney}}: $73$ == ;Alphabetical Arithmetic {{:Henry Ernest Dudeney/Modern Puzzles/73 - Alphabetical Arithmetic}} == Solution == <pre> 9 3 Less 1 7 multiplied by 4 = 6 8 --- Leaving 2 5 --- </pre> == Proof == Immediately: :$F > D$ :$A \le 4$ {{finish}} == Sources == * {{BookRefer...")
- 20:24, 7 December 2021 Caliburn talk contribs created page Signed Measure of Limit of Increasing Sequence of Measurable Sets (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma}$ be a measurable space. Let $\mu$ be a signed measure on $\struct {X, \Sigma}$. Let $E \in \Sigma$. Let $\sequence {E_n}_{n \mathop \in \N}$ be an increasing sequence of $\Sigma$-measurable sets such that: :$E_n \uparrow E$ where $E_n \uparrow E$ denotes the Definition:Limit...")
- 20:16, 7 December 2021 Caliburn talk contribs created page Measure of Limit of Increasing Sequence of Measurable Sets (extracting from Characterization of Measures)
- 19:43, 7 December 2021 Caliburn talk contribs created page Category:Jordan Decomposition Theorem (Created page with "Category:Signed Measures")
- 19:42, 7 December 2021 Caliburn talk contribs created page Jordan Decomposition Theorem/Lemma (Created page with "== Lemma == Let $\struct {X, \Sigma}$ be a measurable space. Let $\mu$ be a signed measure on $\struct {X, \Sigma}$. Let $\tuple {P, N}$ be a Hahn decomposition of $\mu$. For each $A \in \Sigma$, define: :$\map {\mu^+} A = \map \mu {P \cap A}$ and: :$\map {\mu^-} A = -\map \mu {P \cap N}$ Then: <onlyinclude> :$\mu^+$ and $\mu^-$ are Definition:Signed Measure|signed...")
- 19:33, 7 December 2021 Prime.mover talk contribs created page Category:Definitions/Named Definitions/Tits (Created page with "{{NameCategoryDef|Jacques Tits}}")
- 19:33, 7 December 2021 Prime.mover talk contribs created page Category:Named Theorems/Tits (Created page with "{{NameCategory|Jacques Tits}}")
- 19:32, 7 December 2021 Prime.mover talk contribs created page Mathematician:Jacques Tits (Created page with "== Mathematician == <onlyinclude> Belgian, then French mathematician who worked on group theory and incidence geometry. </onlyinclude> == Nationality == Belgian, then French == History == * Born: 12 August 1930 in Uccle, Belgium * Died: 5 December 2021 == Theorems and Definitions == * Tits Alternative * Tits Building * Tits Group * Tits Metric {{NameCategoryLink|Tits}} {{NameC...")
- 18:30, 7 December 2021 Caliburn talk contribs created page User:Caliburn/s/mt/Horizontal Section of Set Difference is Set Difference of Horizontal Sections (Created page with "== Theorem == <onlyinclude> :$\paren {E_1 \setminus E_2}^y = E_1^y \setminus E_2^y$ </onlyinclude> == Proof == Note that: :$x \in E_1^y \setminus E_2^y$ This is equivalent to: :$x \in E_1^y$ and $x \not \in E_2^y$. That is: :$\tuple {x, y} \in E_1$ and $\tuple {x, y} \not \in E_2$ This is the case {{iff}}: :$\tuple {x, y} \in E_1 \setminus E_2$ Which is equivalent to: :$x \in \paren {E_1 \setminus E_2}^y$ So we have: :$x \in E_1^y \setminus E_2^y$ {{iff...")
- 18:02, 7 December 2021 Caliburn talk contribs created page Vertical Section of Measurable Set is Measurable (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma_X}$ and $\struct {Y, \Sigma_Y}$ be measurable spaces. Let $E \in \Sigma_X \otimes \Sigma_Y$ where $\Sigma_X \otimes \Sigma_Y$ is the product $\sigma$-algebra of $\Sigma_X$ and $\Sigma_Y$. Let $x \in X$. Then: :$E_x \in \Sigma_Y$ where $E_x$ is the $x$-vertical section of $E$. </onlyinclude> == Proof ==...")
- 17:55, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Horizontal Section of Set is Measurable to Horizontal Section of Measurable Set is Measurable without leaving a redirect
- 17:40, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Complement of Vertical Section of Set is Vertical Section of Complement to Complement of Vertical Section of Set is Vertical Section of Complement without leaving a redirect
- 17:37, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Complement of Horizontal Section of Set is Horizontal Section of Complement to Complement of Horizontal Section of Set is Horizontal Section of Complement without leaving a redirect
- 17:33, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Union of Vertical Sections is Vertical Section of Union to Union of Vertical Sections is Vertical Section of Union without leaving a redirect
- 17:33, 7 December 2021 Caliburn talk contribs created page Category:Vertical Section of Sets (Created page with "{{SubjectCategoryNodef|Vertical Section of Set}} Category:Measure Theory")
- 14:37, 7 December 2021 Caliburn talk contribs created page User:Caliburn/s/mt/Radon-Nikodym Theorem (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma}$ be a measurable space. Let $\mu$ and $\nu$ be $\sigma$-finite measures on $\struct {X, \Sigma}$ such that: :$\nu$ is absolutely continuous with respect to $\mu$. Then there exists a $\Sigma$-measurable function $g : X \to \hointr 0 \infty$ such that: :$\ds \map \nu...")
- 14:29, 7 December 2021 Caliburn talk contribs created page User:Caliburn/s/mt/Characterization of Absolutely Continuous Measures (Created page with "== Theorem == <onlyinclude> Let $\struct {X, \Sigma}$ be a measurable space. Let $\mu$ be a measure on $\struct {X, \Sigma}$. Let $\nu$ be a finite measure on $\struct {X, \Sigma}$. Then $\nu$ is absolutely continuous with respect to $\mu$ {{iff}}: :for each $\epsilon > 0$ there exists $\delta > 0$ such that for each $A \in \Sigma$ with $\...")
- 14:10, 7 December 2021 Caliburn talk contribs created page Category:Uniqueness of Jordan Decomposition (Created page with "Category:Signed Measures")
- 14:08, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Uniqueness of Jordan Decomposition/Lemma to Uniqueness of Jordan Decomposition/Lemma without leaving a redirect
- 14:08, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Uniqueness of Jordan Decomposition to Uniqueness of Jordan Decomposition without leaving a redirect
- 14:04, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Definition:Positive Part of Signed Measure to Definition:Positive Part of Signed Measure without leaving a redirect
- 14:03, 7 December 2021 Caliburn talk contribs moved page User:Caliburn/s/mt/Definition:Jordan Decomposition to Definition:Jordan Decomposition without leaving a redirect