List questions from lebesgue-measure

Published on 25 Mar 2026 - 13:53

57

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A Lebesgue integral into a sum

Published on 11 Apr 2026 - 1:12

170

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Polygons are Jordan Measurable in $\mathbb R^2$

Published on 12 Apr 2026 - 6:36

31

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Why require open supersets in definition of Lebesgue measurability

Published on 11 Apr 2026 - 22:37

141

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Is the Lebesgue Measure on $[a,b]$ perfect?

Published on 28 Mar 2026 - 10:16

94

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Is the Lebesgue measure on $[a,b]$ $(\subset \mathbb{R})$ perfect?

Published on 28 Mar 2026 - 12:02

93

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Suppose $f \in L^1([0,1],\lambda)$ and let $\alpha \in (0,1)$. Assume that $\int_E f=0$ for all$E$ s.t $m(E)=\alpha$ show $f=0$ a.e

Published on 20 Jan 2020 - 22:45

67

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Excising a compact subset of a set of finite Lebesgue measure

Published on 12 Apr 2026 - 16:47

35

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About two measurable set question

Published on 07 Apr 2026 - 19:40

43

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Prove that: $\lambda^{d}(s_{a}(M))=a^{d}\lambda^{d}(M)$ for any lebesgue-measurable set where $s_{a}(M)=aM$

Published on 21 Jan 2020 - 16:35

93

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Non-uniformly integrable function

Published on 10 Apr 2026 - 18:43

178

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there exists a measurable set $A$ such that $f = \chi_{A}$ a.e.

Published on 04 Apr 2026 - 4:37

589

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Show that there is a countable disjoint collection $\{ I_k \}_{k = 1}^{\infty}$ of intervals

Published on 22 Jan 2020 - 13:01

134

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Is $f(x) = \frac{\cos(x)}{x}$ Lebesgue integrable over $E = [0,1]$?

Published on 04 Apr 2026 - 4:39

636

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Continuous functions with compact support are dense in $L^1$ (Hypotheses)

Published on 11 Apr 2026 - 12:19

List Question

Does the Dominated Convergence Theorem Hold Almost Surely.

A Lebesgue integral into a sum

Polygons are Jordan Measurable in $\mathbb R^2$

Why require open supersets in definition of Lebesgue measurability

Is the Lebesgue Measure on $[a,b]$ perfect?

Is the Lebesgue measure on $[a,b]$ $(\subset \mathbb{R})$ perfect?

Suppose $f \in L^1([0,1],\lambda)$ and let $\alpha \in (0,1)$. Assume that $\int_E f=0$ for all$E$ s.t $m(E)=\alpha$ show $f=0$ a.e

Excising a compact subset of a set of finite Lebesgue measure

About two measurable set question

Prove that: $\lambda^{d}(s_{a}(M))=a^{d}\lambda^{d}(M)$ for any lebesgue-measurable set where $s_{a}(M)=aM$

Non-uniformly integrable function

there exists a measurable set $A$ such that $f = \chi_{A}$ a.e.

Show that there is a countable disjoint collection $\{ I_k \}_{k = 1}^{\infty}$ of intervals

Is $f(x) = \frac{\cos(x)}{x}$ Lebesgue integrable over $E = [0,1]$?

Continuous functions with compact support are dense in $L^1$ (Hypotheses)

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