Question

Constructing a regular measure from a set-function of open sets

score 27 · Answer 1 · 2026-03-28 10:14:55

27

Views

Constructing a regular measure from a set-function of open sets

Published on 28 Mar 2026 - 10:14

score 2.8k · Answer 2 · 2026-03-28 17:04:39

2.8k

Views

Subset of the preimage of a semicontinuous real function is Borel

Published on 28 Mar 2026 - 17:04

score 81 · Answer 3 · 2011-11-15 22:06:43

81

Views

Set measurability from function measurability Borel-wise

Published on 15 Nov 2011 - 22:06

score 12k · Answer 4 · 2026-03-27 15:05:31

12k

Views

Is "product" of Borel sigma algebras the Borel sigma algebra of the "product" of underlying topologies?

Published on 27 Mar 2026 - 15:05

score 18.1k · Answer 5 · 2012-12-06 17:18:23

18.1k

Views

Are Monotone functions Borel Measurable?

Published on 06 Dec 2012 - 17:18

score 34 · Answer 6 · 2020-07-31 21:08:19

34

Views

Problem with showing that any nonempty open subset of plane is not contained in countable sum of segments and usage of this fact

Published on 31 Jul 2020 - 21:08

score 48 · Answer 7 · 2020-08-02 17:11:20

48

Views

Prove that $\mathcal M : = \left \{E \in \mathcal B_{\Bbb R^2}\ |\ \lambda_{\Bbb R^2} (E+x) = \lambda_{\Bbb R^2} (E) \right \}$ is a monotone class.

Published on 02 Aug 2020 - 17:11

score 41 · Answer 8 · 2020-08-03 10:48:02

41

Views

Problem with showing existance of countable family of Borel subsets, equivalence relation

Published on 03 Aug 2020 - 10:48

score 518 · Answer 9 · 2020-08-07 01:47:11

518

Views

Is $f:\mathbb{R}^2\to\mathbb{R}$ defined by $f(x,y)=xy$ Borel-measurable?

Published on 07 Aug 2020 - 1:47

score 1.4k · Answer 10 · 2020-08-08 10:32:51

1.4k

Views

$\sigma$-algebra generated by open balls

Published on 08 Aug 2020 - 10:32

score 77 · Answer 11 · 2020-08-08 16:20:12

77

Views

$ {{\int} f(\textbf {xt})\ d\lambda_{\Bbb R^2} (\textbf {t}) = |xy| {\int} f(\textbf {t})\ d\lambda_{\Bbb R^2} (\textbf {t})}.$

Published on 08 Aug 2020 - 16:20

score 870 · Answer 12 · 2020-08-10 21:37:39

870

Views

Borel sets as the countable intersection of open sets

Published on 10 Aug 2020 - 21:37

score 173 · Answer 13 · 2020-08-11 22:27:20

173

Views

Image of a Borel set under monotonic functions

Published on 11 Aug 2020 - 22:27

score 59 · Answer 14 · 2026-03-25 23:38:05

59

Views

Show that $\{x\}\in \mathbb{B}(X)$ for every $x\in X$

Published on 25 Mar 2026 - 23:38

score 448 · Answer 15 · 2026-03-28 10:16:17

448

Views

Example of borel measurable function for which there doesnot exist a borel set such that function restricted on it is continuous

Published on 28 Mar 2026 - 10:16

List Question

Constructing a regular measure from a set-function of open sets

Subset of the preimage of a semicontinuous real function is Borel

Set measurability from function measurability Borel-wise

Is "product" of Borel sigma algebras the Borel sigma algebra of the "product" of underlying topologies?

Are Monotone functions Borel Measurable?

Problem with showing that any nonempty open subset of plane is not contained in countable sum of segments and usage of this fact

Prove that $\mathcal M : = \left \{E \in \mathcal B_{\Bbb R^2}\ |\ \lambda_{\Bbb R^2} (E+x) = \lambda_{\Bbb R^2} (E) \right \}$ is a monotone class.

Problem with showing existance of countable family of Borel subsets, equivalence relation

Is $f:\mathbb{R}^2\to\mathbb{R}$ defined by $f(x,y)=xy$ Borel-measurable?

$\sigma$-algebra generated by open balls

$ {{\int} f(\textbf {xt})\ d\lambda_{\Bbb R^2} (\textbf {t}) = |xy| {\int} f(\textbf {t})\ d\lambda_{\Bbb R^2} (\textbf {t})}.$

Borel sets as the countable intersection of open sets

Image of a Borel set under monotonic functions

Show that $\{x\}\in \mathbb{B}(X)$ for every $x\in X$

Example of borel measurable function for which there doesnot exist a borel set such that function restricted on it is continuous

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