Question

A countable union (intersection) of closed (open) sets is a Borel set - Questions

score 576 · Answer 1 · 2020-10-08 14:19:01

576

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A countable union (intersection) of closed (open) sets is a Borel set - Questions

Published on 08 Oct 2020 - 14:19

score 499 · Answer 2 · 2020-10-09 08:34:27

499

Views

Is A Borel set either a $G_\delta$ or a $F_\sigma$?

Published on 09 Oct 2020 - 8:34

score 29 · Answer 3 · 2020-10-18 22:54:16

29

Views

Is S a $\sigma$-alegrba?

Published on 18 Oct 2020 - 22:54

score 48 · Answer 4 · 2026-03-28 13:41:38

48

Views

Nontrivial Signed Measure on Lebesgue Measurable Sets Being Trivial on Borel Sets

Published on 28 Mar 2026 - 13:41

score 173 · Answer 5 · 2026-03-28 11:54:16

173

Views

Prove that $f$ is one-to-one on $B$ and $f^{-1}:Y\to B$ is Borel.

Published on 28 Mar 2026 - 11:54

score 143 · Answer 6 · 2026-03-28 11:54:12

143

Views

Showing $\mu_f$ is a measure on the $\sigma-$algebra $\mathcal{B}$ of Borel subsets of $\mathbb{R}.$

Published on 28 Mar 2026 - 11:54

score 415 · Answer 7 · 2026-03-28 12:02:45

415

Views

Are slices of Borel sets also Borel sets?

Published on 28 Mar 2026 - 12:02

score 825 · Answer 8 · 2020-10-30 16:31:33

825

Views

Show that there exists a set $E \in \mathbb{R} \times \mathbb{R}$ such that the cross sections are borel sets, but $E \notin B\otimes B$

Published on 30 Oct 2020 - 16:31

score 262 · Answer 9 · 2020-11-02 18:55:14

262

Views

(clarify this answer?) Prove that for all subsets of the reals A, there exists a Borel set $A \subset B$ such that $\lambda(B) = \lambda^*(A) $

Published on 02 Nov 2020 - 18:55

score 1.5k · Answer 10 · 2020-11-03 20:00:35

1.5k

Views

Showing $(\Omega, \mathcal{F}, P)$ is a probability space.

Published on 03 Nov 2020 - 20:00

score 460 · Answer 11 · 2020-11-04 08:29:32

460

Views

A set in the Borel $\sigma$-algebra over $[0,1]$ that isn't in the algebra generated by open sets

Published on 04 Nov 2020 - 8:29

score 103 · Answer 12 · 2020-11-04 18:33:36

103

Views

what is difference between Borel algebra and Borel σ-algebra?

Published on 04 Nov 2020 - 18:33

score 258 · Answer 13 · 2020-11-07 13:42:42

258

Views

Subsequence such that integrals converge over any Borel set in $[0,1]$

Published on 07 Nov 2020 - 13:42

score 136 · Answer 14 · 2020-11-08 15:43:21

136

Views

Prove that this set is a borel set

Published on 08 Nov 2020 - 15:43

score 3k · Answer 15 · 2020-11-08 21:10:11

3k

Views

Is every Borel set a countable union of intervals?

Published on 08 Nov 2020 - 21:10

List Question

A countable union (intersection) of closed (open) sets is a Borel set - Questions

Is A Borel set either a $G_\delta$ or a $F_\sigma$?

Is S a $\sigma$-alegrba?

Nontrivial Signed Measure on Lebesgue Measurable Sets Being Trivial on Borel Sets

Prove that $f$ is one-to-one on $B$ and $f^{-1}:Y\to B$ is Borel.

Showing $\mu_f$ is a measure on the $\sigma-$algebra $\mathcal{B}$ of Borel subsets of $\mathbb{R}.$

Are slices of Borel sets also Borel sets?

Show that there exists a set $E \in \mathbb{R} \times \mathbb{R}$ such that the cross sections are borel sets, but $E \notin B\otimes B$

(clarify this answer?) Prove that for all subsets of the reals A, there exists a Borel set $A \subset B$ such that $\lambda(B) = \lambda^*(A) $

Showing $(\Omega, \mathcal{F}, P)$ is a probability space.

A set in the Borel $\sigma$-algebra over $[0,1]$ that isn't in the algebra generated by open sets

what is difference between Borel algebra and Borel σ-algebra?

Subsequence such that integrals converge over any Borel set in $[0,1]$

Prove that this set is a borel set

Is every Borel set a countable union of intervals?

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