List questions from measurable-functions

Published on 26 Mar 2026 - 6:21

537

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The Hardy–Littlewood maximal function is Borel measurable

Published on 26 Sep 2022 - 18:01

69

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No generalization of subadditivity for limit superior like Fatou's lemma.

Published on 27 Feb 2026 - 11:22

155

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A question about Atoms in Measure Theory

Published on 26 Mar 2026 - 16:05

56

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Extend Pettis's measurability theorem to $\sigma$-finite measure spaces

Published on 06 Oct 2022 - 7:17

109

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Application of Egoroff's Theorem in $M$-measurable functions

Published on 07 Oct 2022 - 0:03

36

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Measurability of an absolutely continuous random variable

Published on 07 Oct 2022 - 16:06

35

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Borel $\sigma$-algebra of a perfectly normal space is the smallest $\sigma$-algebra such that every continuous function is Borel measurable

Published on 09 Oct 2022 - 20:19

45

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Radon-Nikodym derivative composed with a measurable function

Published on 24 Feb 2026 - 15:23

49

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Show $\mathbb{P}_B \ll \mathbb{P}$ and find f s.t. $\mathbb{P}_B= f\mathbb{P}$

Published on 14 Oct 2022 - 21:54

310

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When inverse of measurable function also measurable?

Published on 17 Oct 2022 - 9:52

181

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Measurable argmax correspondence on probability spaces

Published on 23 Feb 2026 - 5:59

40

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Is there a Borel set $B \in \mathcal B_E$ such that $B \subset \operatorname{im} f$ and $\nu (B) = 1$?

Published on 20 Oct 2022 - 10:24

55

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If $f:\mathbb{R}\to\mathbb{R}$ is continuous almost everywhere and $X$ is a random variable, then is $f(X)$ a random variable?

Published on 21 Oct 2022 - 8:54

101

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Hausdorff topological spaces: Is the pointwise limit of a sequence of Borel measurable functions again Borel measurable?

Published on 24 Oct 2022 - 11:45

List Question

Confusion about a proof of Lusin's theorem

The Hardy–Littlewood maximal function is Borel measurable

No generalization of subadditivity for limit superior like Fatou's lemma.

A question about Atoms in Measure Theory

Extend Pettis's measurability theorem to $\sigma$-finite measure spaces

Application of Egoroff's Theorem in $M$-measurable functions

Measurability of an absolutely continuous random variable

Borel $\sigma$-algebra of a perfectly normal space is the smallest $\sigma$-algebra such that every continuous function is Borel measurable

Radon-Nikodym derivative composed with a measurable function

Show $\mathbb{P}_B \ll \mathbb{P}$ and find f s.t. $\mathbb{P}_B= f\mathbb{P}$

When inverse of measurable function also measurable?

Measurable argmax correspondence on probability spaces

Is there a Borel set $B \in \mathcal B_E$ such that $B \subset \operatorname{im} f$ and $\nu (B) = 1$?

If $f:\mathbb{R}\to\mathbb{R}$ is continuous almost everywhere and $X$ is a random variable, then is $f(X)$ a random variable?

Hausdorff topological spaces: Is the pointwise limit of a sequence of Borel measurable functions again Borel measurable?

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