Question

Prove that $\mathscr{B}(\mathbb{R}^d)$ is a subset of $\mathscr{F}$, a $\sigma$-field

score 181 · Answer 1 · 2026-04-16 15:07:28

181

Views

Prove that $\mathscr{B}(\mathbb{R}^d)$ is a subset of $\mathscr{F}$, a $\sigma$-field

Published on 16 Apr 2026 - 15:07

score 402 · Answer 2 · 2026-04-13 07:05:00

402

Views

$A+B$ Borel set if $A$ is countable, open.

Published on 13 Apr 2026 - 7:05

score 1.5k · Answer 3 · 2026-04-16 14:27:37

1.5k

Views

If $X$ is a Borel set and $f$ has countably many discontinuities, prove that $f:X\rightarrow \mathbf{R}$ is Borel measurable.

Published on 16 Apr 2026 - 14:27

score 38 · Answer 4 · 2026-05-10 14:04:45

38

Views

Determining whether an interval (0,1] $\in\mathfrak B(\mathbb R)$ or not.

Published on 10 May 2026 - 14:04

score 235 · Answer 5 · 2026-04-16 17:19:40

235

Views

Examples of functions that are not Borel measurable that will be accessible to 1st year undergraduates

Published on 16 Apr 2026 - 17:19

score 222 · Answer 6 · 2026-05-10 16:02:17

222

Views

What sets are obtained by adding $\aleph_1$ unions and intersections to the Borel algebra?

Published on 10 May 2026 - 16:02

score 1.7k · Answer 7 · 2026-05-10 14:06:00

1.7k

Views

Is the Borel sigma algebra complete under some measure?

Published on 10 May 2026 - 14:06

score 487 · Answer 8 · 2026-04-16 00:23:02

487

Views

If $E$ is Lebesgue-measurable, then Borel sets exist with $B_1 \subset E \subset B_2$

Published on 16 Apr 2026 - 0:23

score 439 · Answer 9 · 2026-05-10 16:02:37

439

Views

Example of a Lebesgue measurable set that can't be constructed from Borel sets and projections?

Published on 10 May 2026 - 16:02

score 991 · Answer 10 · 2026-04-16 08:31:17

991

Views

Are all convex sets Borel sets?

Published on 16 Apr 2026 - 8:31

score 57 · Answer 11 · 2026-04-16 09:31:04

57

Views

Show $\sigma ( \tau) = \sigma ( A)$ as an alternative formulation of Borel $\sigma -$Algebra

Published on 16 Apr 2026 - 9:31

score 167 · Answer 12 · 2026-04-11 14:47:53

167

Views

Are all Jordan measurable sets Borel?

Published on 11 Apr 2026 - 14:47

score 674 · Answer 13 · 2026-04-13 17:37:31

674

Views

What is the Sigma Algebra generated by Jordan measurable sets?

Published on 13 Apr 2026 - 17:37

score 458 · Answer 14 · 2026-04-12 23:58:26

458

Views

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Published on 12 Apr 2026 - 23:58

score 194 · Answer 15 · 2026-05-10 14:04:52

194

Views

A continuous Function from $R$ to a Banach Space is Borel-Measurable

Published on 10 May 2026 - 14:04

List Question

Prove that $\mathscr{B}(\mathbb{R}^d)$ is a subset of $\mathscr{F}$, a $\sigma$-field

$A+B$ Borel set if $A$ is countable, open.

If $X$ is a Borel set and $f$ has countably many discontinuities, prove that $f:X\rightarrow \mathbf{R}$ is Borel measurable.

Determining whether an interval (0,1] $\in\mathfrak B(\mathbb R)$ or not.

Examples of functions that are not Borel measurable that will be accessible to 1st year undergraduates

What sets are obtained by adding $\aleph_1$ unions and intersections to the Borel algebra?

Is the Borel sigma algebra complete under some measure?

If $E$ is Lebesgue-measurable, then Borel sets exist with $B_1 \subset E \subset B_2$

Example of a Lebesgue measurable set that can't be constructed from Borel sets and projections?

Are all convex sets Borel sets?

Show $\sigma ( \tau) = \sigma ( A)$ as an alternative formulation of Borel $\sigma -$Algebra

Are all Jordan measurable sets Borel?

What is the Sigma Algebra generated by Jordan measurable sets?

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

A continuous Function from $R$ to a Banach Space is Borel-Measurable

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