Question

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

score 179 · Answer 1 · 2026-03-25 03:03:00

179

Views

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

Published on 25 Mar 2026 - 3:03

score 399 · Answer 2 · 2018-10-09 15:32:04

399

Views

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

Published on 09 Oct 2018 - 15:32

score 1.5k · Answer 3 · 2018-10-18 08:11:37

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 18 Oct 2018 - 8:11

score 35 · Answer 4 · 2026-03-25 01:22:37

35

Views

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

Published on 25 Mar 2026 - 1:22

score 232 · Answer 5 · 2018-10-24 17:57:26

232

Views

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

Published on 24 Oct 2018 - 17:57

score 216 · Answer 6 · 2018-10-25 03:17:44

216

Views

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

Published on 25 Oct 2018 - 3:17

score 1.7k · Answer 7 · 2026-03-25 03:01:17

1.7k

Views

Is the Borel sigma algebra complete under some measure?

Published on 25 Mar 2026 - 3:01

score 484 · Answer 8 · 2018-10-25 14:00:15

484

Views

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

Published on 25 Oct 2018 - 14:00

score 435 · Answer 9 · 2018-10-26 00:00:09

435

Views

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

Published on 26 Oct 2018 - 0:00

score 987 · Answer 10 · 2018-10-26 21:49:05

987

Views

Are all convex sets Borel sets?

Published on 26 Oct 2018 - 21:49

score 54 · Answer 11 · 2018-10-30 19:10:32

54

Views

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

Published on 30 Oct 2018 - 19:10

score 164 · Answer 12 · 2018-10-31 13:30:39

164

Views

Are all Jordan measurable sets Borel?

Published on 31 Oct 2018 - 13:30

score 671 · Answer 13 · 2018-10-31 14:03:32

671

Views

What is the Sigma Algebra generated by Jordan measurable sets?

Published on 31 Oct 2018 - 14:03

score 455 · Answer 14 · 2018-10-31 20:26:55

455

Views

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

Published on 31 Oct 2018 - 20:26

score 189 · Answer 15 · 2026-03-25 03:00:31

189

Views

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

Published on 25 Mar 2026 - 3:00

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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