List questions from lebesgue-measure

Published on 30 Apr 2026 - 9:13

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An exemple of measurable function $f$ on $\mathbb R^2$ s.t. $f^y$ is not mesurable for every $y$.

Published on 16 Apr 2026 - 18:00

942

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Is a function discrete or continuous w.r.t. to the Lebesgue measure?

Published on 14 Apr 2026 - 20:16

128

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Notations in Banach Tarski paradox proof

Published on 14 Apr 2026 - 4:15

125

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Showing Lebesgue's definition of measure implies measurability

Published on 30 Apr 2026 - 9:13

916

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Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere

Published on 15 Apr 2026 - 17:39

1.4k

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How to prove that $m^*(\phi)=0$

Published on 12 Apr 2026 - 11:32

24

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Given $A\subset [0,1]$ prove that $m^(\{1-x:x\in A \})=m^ (A)$

Published on 30 Apr 2026 - 9:12

202

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Show that Lebesgue outer measure is not additive even for the finite family of pairwise disjoint sets

Published on 14 Apr 2026 - 9:54

167

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Reference request: Caratheodory Extension Theorem

Published on 16 Apr 2026 - 9:23

463

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A $\mathcal{C}^1$ function $f: \mathbb{R} \rightarrow \mathbb{R} $ preserve Jordan measurability

Published on 16 Apr 2026 - 13:02

72

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approximation of outer measurability

Published on 14 Apr 2026 - 3:46

397

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Is lebesgue measure complete on $\mathcal{B}(\mathbb{R})$?A counter example

Published on 11 Apr 2026 - 20:33

446

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Fubini's theorem and set of measure zero

Published on 14 Apr 2026 - 1:39

116

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Lebesgue measurable function question

Published on 30 Apr 2026 - 10:21

List Question

Showing Convergence of Positive Series

An exemple of measurable function $f$ on $\mathbb R^2$ s.t. $f^y$ is not mesurable for every $y$.

Is a function discrete or continuous w.r.t. to the Lebesgue measure?

Notations in Banach Tarski paradox proof

Showing Lebesgue's definition of measure implies measurability

Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere

How to prove that $m^*(\phi)=0$

Given $A\subset [0,1]$ prove that $m^(\{1-x:x\in A \})=m^ (A)$

Show that Lebesgue outer measure is not additive even for the finite family of pairwise disjoint sets

Reference request: Caratheodory Extension Theorem

A $\mathcal{C}^1$ function $f: \mathbb{R} \rightarrow \mathbb{R} $ preserve Jordan measurability

approximation of outer measurability

Is lebesgue measure complete on $\mathcal{B}(\mathbb{R})$?A counter example

Fubini's theorem and set of measure zero

Lebesgue measurable function question

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