List questions from lebesgue-measure

Published on 28 Mar 2026 - 12:13

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Does there exists a $\mathbb{Q}$ vector space automorphism of $\mathbb{R}$ which is not Lebesgue measurable?

Published on 25 Mar 2026 - 3:02

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Homeomorphism of Borel set is Borel

Published on 27 Jun 2018 - 2:31

1.9k

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How to prove every open set is Lebesgue measurable?

Published on 27 Jun 2018 - 15:57

72

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Integration over level sets

Published on 27 Jun 2018 - 16:00

604

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$f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$,

Published on 25 Mar 2026 - 20:12

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Cavalieri's Principle

Published on 30 Jun 2018 - 18:01

39

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Can we expect that $\sum_{n\in \mathbb Z^d} |\hat{f}(x-An)|^2 \leq C \|f\|_{L^2}$?

Published on 30 Jun 2018 - 22:00

82

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In $\int f d \mu_1 = \mu_2 (\{(x,y) \in D \times V )| 0\leq y \leq f(x)\}), f: D\rightarrow V, f\geq 0$?

Published on 26 Mar 2026 - 9:21

239

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For E of finite Lebesgue measure, is $f(t) = \int_E \cos(tx) dx$

Published on 02 Jul 2018 - 21:13

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Verifying piecewise function is Lebesgue integrable

Published on 26 Mar 2026 - 9:25

583

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Equality between the measure of a compact set and the limit of a series of open sets

Published on 03 Jul 2018 - 1:17

1.7k

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Example of a set that is $F_\sigma$ but not $G_\delta$

Published on 03 Jul 2018 - 1:27

583

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Every open set $ G \subset \mathbb{R}^n$ can be approximated by finite union of non-degenerate compact intervals contained in $G$?

Published on 04 Jul 2018 - 5:35

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Application of Borel Cantelli Lemma 1

Published on 25 Mar 2026 - 12:53

List Question

A question about Egoroff theorem

Does there exists a $\mathbb{Q}$ vector space automorphism of $\mathbb{R}$ which is not Lebesgue measurable?

Homeomorphism of Borel set is Borel

How to prove every open set is Lebesgue measurable?

Integration over level sets

$f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$,

Cavalieri's Principle

Can we expect that $\sum_{n\in \mathbb Z^d} |\hat{f}(x-An)|^2 \leq C \|f\|_{L^2}$?

In $\int f d \mu_1 = \mu_2 (\{(x,y) \in D \times V )| 0\leq y \leq f(x)\}), f: D\rightarrow V, f\geq 0$?

For E of finite Lebesgue measure, is $f(t) = \int_E \cos(tx) dx$

Verifying piecewise function is Lebesgue integrable

Equality between the measure of a compact set and the limit of a series of open sets

Example of a set that is $F_\sigma$ but not $G_\delta$

Every open set $ G \subset \mathbb{R}^n$ can be approximated by finite union of non-degenerate compact intervals contained in $G$?

Application of Borel Cantelli Lemma 1

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