List questions from lebesgue-measure

Published on 10 Apr 2026 - 6:43

85

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Existence of non-randomized most powerful test

Published on 10 Apr 2026 - 3:19

688

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Lebesgue Measure of open ball in $\mathbb{R}^n$

Published on 12 Apr 2026 - 11:05

160

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For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

Published on 17 Apr 2026 - 5:41

59

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Application of Egoroff's thm on infinite measure

Published on 12 Apr 2026 - 15:45

115

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Lebesgue measurable function on interval

Published on 14 Apr 2026 - 8:12

46

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How can I show if an incremental function is Lebesgue measurable?

Published on 10 Apr 2026 - 13:27

93

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$\lim_{\lambda \to \infty}\dfrac{1}{\lambda}\int_0^{\lambda}yf(y)dy = 0$?

Published on 12 Apr 2026 - 2:09

635

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Borel measurable functions equal almost everywhere

Published on 25 Mar 2026 - 13:53

44

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Lebesgue integration over domains

Published on 12 Apr 2026 - 4:58

219

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The case of Young's inequality for convolution for $1\leq p\leq 2$ implies the case $p\geq 2$

Published on 17 Apr 2026 - 9:08

91

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Support of a measure and Lebesgue decomposition

Published on 09 Apr 2026 - 7:09

104

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Discussing a problem with Riemann integral.

Published on 11 Apr 2026 - 3:47

109

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Measure convergence and pointwise convergence in almost everywhere

Published on 12 Apr 2026 - 15:41

101

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For $f \in L^1_{\text{loc}}(\Bbb{R}^d)$ the average $x \mapsto \frac1{\lambda(B(x,r))} \int_{B(x,r)} f(y)\,dy$ is measurable

Published on 16 Apr 2026 - 19:14

List Question

Is the indicator function of rational numbers integrable?

Existence of non-randomized most powerful test

Lebesgue Measure of open ball in $\mathbb{R}^n$

For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

Application of Egoroff's thm on infinite measure

Lebesgue measurable function on interval

How can I show if an incremental function is Lebesgue measurable?

$\lim_{\lambda \to \infty}\dfrac{1}{\lambda}\int_0^{\lambda}yf(y)dy = 0$?

Borel measurable functions equal almost everywhere

Lebesgue integration over domains

The case of Young's inequality for convolution for $1\leq p\leq 2$ implies the case $p\geq 2$

Support of a measure and Lebesgue decomposition

Discussing a problem with Riemann integral.

Measure convergence and pointwise convergence in almost everywhere

For $f \in L^1_{\text{loc}}(\Bbb{R}^d)$ the average $x \mapsto \frac1{\lambda(B(x,r))} \int_{B(x,r)} f(y)\,dy$ is measurable

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