Question

Weak Compactness Theorem for Borel Measures

score 343 · Answer 1 · 2026-03-29 14:55:49

343

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Weak Compactness Theorem for Borel Measures

Published on 29 Mar 2026 - 14:55

score 65 · Answer 2 · 2022-05-12 09:01:23

65

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Show that $f = \sum_{k=1}^{\infty} \frac{1}{k} \mathbb{1}_{A_k}$ is a representation for a measurable function

Published on 12 May 2022 - 9:01

score 112 · Answer 3 · 2022-05-18 22:32:11

112

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Show that Borel-$\sigma$-algebra on $\mathbb{R}^n$ includes open sets

Published on 18 May 2022 - 22:32

score 350 · Answer 4 · 2022-05-20 22:47:45

350

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Exemple where tower property of conditional expectation is NOT verify

Published on 20 May 2022 - 22:47

score 52 · Answer 5 · 2026-03-29 14:59:23

52

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If $A\in\mathfrak{M}$, then there exist Borel sets $F$ and $G$ such that $F\subset A\subset G$, and $\mu(G-A)=\mu(A-F)=0$.

Published on 29 Mar 2026 - 14:59

score 59 · Answer 6 · 2022-06-01 20:04:06

59

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step function measurable proof

Published on 01 Jun 2022 - 20:04

score 117 · Answer 7 · 2022-06-13 09:39:30

117

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Existence of Borel sigma Algebra

Published on 13 Jun 2022 - 9:39

score 36 · Answer 8 · 2022-06-15 21:05:27

36

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Borel's Hierarchy of $\bigcup _{n\in \mathbb{N}}[\frac{1}{n+2},\frac{1}{n+1})$

Published on 15 Jun 2022 - 21:05

score 61 · Answer 9 · 2022-06-21 20:32:07

61

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How can I prove that the cardinality of $\Sigma_{\alpha}^{0}$ is $2^{\aleph_{0}}$ for every $\alpha < \omega_{1}$?

Published on 21 Jun 2022 - 20:32

score 102 · Answer 10 · 2022-06-22 00:21:44

102

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Definition of measurable function - connection with being measurable

Published on 22 Jun 2022 - 0:21

score 38 · Answer 11 · 2026-03-27 23:01:32

38

Views

Does $\inf_{B \in \Lambda} \varphi(B) = \varphi\left( \inf_{B \in \Lambda} \right)$ if $\varphi$ is Borel measurable and each $B \in \Lambda$ is Borel

Published on 27 Mar 2026 - 23:01

score 61 · Answer 12 · 2026-03-27 23:31:22

61

Views

Topological Condition ensuring that the Diagonal is measurable

Published on 27 Mar 2026 - 23:31

score 97 · Answer 13 · 2022-07-12 05:40:52

97

Views

Does a "Borel Set" mean "Collection of States"?

Published on 12 Jul 2022 - 5:40

score 35 · Answer 14 · 2022-07-19 14:24:24

35

Views

Need explanation of proof of Theorem 3 in Section 31, Chapter II of Kuratowski's Topology

Published on 19 Jul 2022 - 14:24

score 31 · Answer 15 · 2026-03-28 12:14:52

31

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The product $\sigma$-algebra $\bigotimes _{n\in\mathbb{N}}\mathfrak{B}$ contains the sets of all bounded, monotone and convergent real sequences

Published on 28 Mar 2026 - 12:14

List Question

Weak Compactness Theorem for Borel Measures

Show that $f = \sum_{k=1}^{\infty} \frac{1}{k} \mathbb{1}_{A_k}$ is a representation for a measurable function

Show that Borel-$\sigma$-algebra on $\mathbb{R}^n$ includes open sets

Exemple where tower property of conditional expectation is NOT verify

If $A\in\mathfrak{M}$, then there exist Borel sets $F$ and $G$ such that $F\subset A\subset G$, and $\mu(G-A)=\mu(A-F)=0$.

step function measurable proof

Existence of Borel sigma Algebra

Borel's Hierarchy of $\bigcup _{n\in \mathbb{N}}[\frac{1}{n+2},\frac{1}{n+1})$

How can I prove that the cardinality of $\Sigma_{\alpha}^{0}$ is $2^{\aleph_{0}}$ for every $\alpha < \omega_{1}$?

Definition of measurable function - connection with being measurable

Does $\inf_{B \in \Lambda} \varphi(B) = \varphi\left( \inf_{B \in \Lambda} \right)$ if $\varphi$ is Borel measurable and each $B \in \Lambda$ is Borel

Topological Condition ensuring that the Diagonal is measurable

Does a "Borel Set" mean "Collection of States"?

Need explanation of proof of Theorem 3 in Section 31, Chapter II of Kuratowski's Topology

The product $\sigma$-algebra $\bigotimes _{n\in\mathbb{N}}\mathfrak{B}$ contains the sets of all bounded, monotone and convergent real sequences

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