List questions from lebesgue-measure

Published on 11 Apr 2026 - 18:34

61

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What is the measure of this set?

Published on 25 Mar 2026 - 18:56

247

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Proving Probability Measure Using Dominated Convergence Theorem

Published on 12 Apr 2026 - 8:42

292

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Ham sandwich theorem.

Published on 16 Apr 2026 - 8:56

45

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On the differentiability of increasing functions

Published on 14 Apr 2026 - 4:18

123

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Rudin Real and Complex Analysis Exercise 2.8

Published on 13 Apr 2026 - 8:32

129

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The collection of compactly supported continuous functions is dense in $L^1(\mathbb{R}^d)$.

Published on 16 Apr 2026 - 7:30

43

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Given $a \in (0,1)$, given an example of a Borel set $E \subset \mathbb{R}^2$ with Lebesgue Density $a$?

Published on 11 Apr 2026 - 18:19

110

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Content or measure zero of a graph of a continuous function?

Published on 15 Apr 2026 - 7:47

77

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How large can the range of Lebesgue densities of a measurable subset of $\mathbb{R}$ be?

Published on 11 Apr 2026 - 6:57

114

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Proving Lebesgue measure is translation invariant

Published on 17 Apr 2026 - 12:20

56

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Show $\forall t \in \mathbb{R}$ we have : $F(t) = \int_B \mathbb{1}_A (x-t) d\lambda(x)$

Published on 16 Apr 2026 - 14:58

63

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Proving an inequality for a Lebesgue integrable function

Published on 11 Apr 2026 - 9:17

142

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Deciding whether $f$ is Lebesgue integrable

Published on 16 Apr 2026 - 6:28

46

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Lebesgue integrability of $f_n (x) := \begin{cases} \frac{\lvert\ln (n^7x^2)\rvert}{3+n^4x^2} & x \ne 0 \\ 1 & x=0\end{cases}$ on $\mathbb R$

Published on 16 Apr 2026 - 0:51

List Question

How to show this function is integrable?

What is the measure of this set?

Proving Probability Measure Using Dominated Convergence Theorem

Ham sandwich theorem.

On the differentiability of increasing functions

Rudin Real and Complex Analysis Exercise 2.8

The collection of compactly supported continuous functions is dense in $L^1(\mathbb{R}^d)$.

Given $a \in (0,1)$, given an example of a Borel set $E \subset \mathbb{R}^2$ with Lebesgue Density $a$?

Content or measure zero of a graph of a continuous function?

How large can the range of Lebesgue densities of a measurable subset of $\mathbb{R}$ be?

Proving Lebesgue measure is translation invariant

Show $\forall t \in \mathbb{R}$ we have : $F(t) = \int_B \mathbb{1}_A (x-t) d\lambda(x)$

Proving an inequality for a Lebesgue integrable function

Deciding whether $f$ is Lebesgue integrable

Lebesgue integrability of $f_n (x) := \begin{cases} \frac{\lvert\ln (n^7x^2)\rvert}{3+n^4x^2} & x \ne 0 \\ 1 & x=0\end{cases}$ on $\mathbb R$

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