List questions from borel-sets

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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 22 Apr 2019 - 6:35

67

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

Published on 01 May 2019 - 16:54

2.8k

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Proof borel sets are measurable sets

Published on 25 Mar 2026 - 3:17

121

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Intuition of Standard and Analytic Borel space

Published on 25 Mar 2026 - 13:55

128

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

Published on 10 May 2019 - 13:39

86

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Continuous then measurable?

Published on 25 Mar 2026 - 5:59

193

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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 25 Mar 2026 - 6:06

812

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

Published on 25 Mar 2026 - 13:55

89

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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 25 Mar 2026 - 13:57

269

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

Published on 23 May 2019 - 13:11

192

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

Published on 25 May 2019 - 2:51

203

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Is the interior of a Jordan curve a Borel set?

Published on 28 May 2019 - 8:36

148

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

Published on 25 Mar 2026 - 13:59

562

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

Published on 25 Mar 2026 - 6:08

4.2k

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What is a Borel set?

Published on 05 Jun 2019 - 7:58

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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