List questions from borel-sets

172

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Prove that $\lim_{m(I)\rightarrow 0}\frac{m(E\cap I)}{m(I)}=c$ for some $c$ and moving interval $I$.

Published on 16 Apr 2026 - 13:16

69

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Is there such a term as a "Borel measurable set"?

Published on 14 Apr 2026 - 18:13

2.8k

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Proof borel sets are measurable sets

Published on 10 May 2026 - 17:59

123

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Intuition of Standard and Analytic Borel space

Published on 14 Apr 2026 - 23:22

131

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Exercise about sub-$\sigma$-algebra of $\mathcal{B}(\mathbb{R})$

Published on 14 Apr 2026 - 3:43

92

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Continuous then measurable?

Published on 10 May 2026 - 16:30

196

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Is $f(x)=\begin{cases}\frac{1}{x}, x\neq 0\\ \infty, x=0 \end{cases}$ Borel-measurable? (Using Borel sets)

Published on 10 May 2026 - 16:35

814

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Does every uncountable Borel subset of $\mathbb R$ contains a perfect subset？

Published on 14 Apr 2026 - 22:11

91

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$S(\Bbb{Q}^n)\subseteq \mathcal{P}(\Bbb{Q}^n)$ is Borel and the Borel action of $GL_n(\Bbb{Q})$ on $S(\Bbb{Q}^n)$

Published on 17 Apr 2026 - 4:39

272

Views

Characterization of the Borel $\sigma$-algebra on a topological quotient space

Published on 16 Apr 2026 - 6:15

195

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Understanding definition of random variable in textbook "Basic Stochastic Processes"

Published on 09 Apr 2026 - 14:43

208

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Is the interior of a Jordan curve a Borel set?

Published on 16 Apr 2026 - 22:24

150

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Is the convex hull of a countable set a Borel set?

Published on 12 Apr 2026 - 22:33

565

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$\sigma$-algebra generated by a finite set $S$

Published on 10 May 2026 - 16:32

4.2k

Views

What is a Borel set?

Published on 10 Apr 2026 - 17:31

List Question

Prove that $\lim_{m(I)\rightarrow 0}\frac{m(E\cap I)}{m(I)}=c$ for some $c$ and moving interval $I$.

Is there such a term as a "Borel measurable set"?

Proof borel sets are measurable sets

Intuition of Standard and Analytic Borel space

Exercise about sub-$\sigma$-algebra of $\mathcal{B}(\mathbb{R})$

Continuous then measurable?

Is $f(x)=\begin{cases}\frac{1}{x}, x\neq 0\\ \infty, x=0 \end{cases}$ Borel-measurable? (Using Borel sets)

Does every uncountable Borel subset of $\mathbb R$ contains a perfect subset？

$S(\Bbb{Q}^n)\subseteq \mathcal{P}(\Bbb{Q}^n)$ is Borel and the Borel action of $GL_n(\Bbb{Q})$ on $S(\Bbb{Q}^n)$

Characterization of the Borel $\sigma$-algebra on a topological quotient space

Understanding definition of random variable in textbook "Basic Stochastic Processes"

Is the interior of a Jordan curve a Borel set?

Is the convex hull of a countable set a Borel set?

$\sigma$-algebra generated by a finite set $S$

What is a Borel set?

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