List questions from lebesgue-integral

Published on 09 Apr 2026 - 2:46

39

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How to show $χ_{A∩B}(s)$ and $χ_{A∪B}(s)$ is the min and max respectively

Published on 14 Apr 2026 - 13:20

1.9k

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Tightness + Integrability does not imply uniform integrability?

Published on 14 Apr 2026 - 14:33

1k

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Existence of step function approximation for Lebesgue function in norm by Littlewood's principle

Published on 11 May 2026 - 8:34

187

Views

Suppose $f$ is integrable and $\int_{a}^{x} f = 0,\ \forall x \in [a,b]$ then $f = 0$ almost everywhere.

Published on 16 Apr 2026 - 0:28

492

Views

Integrability of $x^{-a}\log(x)$

Published on 14 Apr 2026 - 2:23

38

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Aggregating and differentiating under integral sign

Published on 14 Apr 2026 - 7:41

154

Views

Functions involving expectations - The dominated/monotone convergence theorem

Published on 16 Apr 2026 - 19:15

2k

Views

Is $L^\infty$ a subset of $L^p$ for finite $p$?

Published on 13 Apr 2026 - 17:00

87

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Moment of measure for Dirac disintegration

Published on 25 Mar 2026 - 15:52

117

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Substitution rule for dirac measure

Published on 11 Apr 2026 - 19:46

254

Views

How to prove that $\mathbf{E}\eta = \int_{0}^{\infty}\mathbf{P}(\{\eta > z\})dz$ for arbitrary non-negative random variable?

Published on 12 Apr 2026 - 1:34

76

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If $f\in L^1([0,\infty ))$ then $\lim_{n\to \infty}\frac{1}{n}\int_{[0,n]}xf(x)dx=0$

Published on 16 Apr 2026 - 0:23

816

Views

$L^1$ function that is not $L^p$ for $p > 1$.

Published on 15 Apr 2026 - 22:48

138

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Lesbesgue theorem for differentiation of indefinite integrals

Published on 13 Apr 2026 - 10:51

List Question

Integral on set $A$

How to show $χ_{A∩B}(s)$ and $χ_{A∪B}(s)$ is the min and max respectively

Tightness + Integrability does not imply uniform integrability?

Existence of step function approximation for Lebesgue function in norm by Littlewood's principle

Suppose $f$ is integrable and $\int_{a}^{x} f = 0,\ \forall x \in [a,b]$ then $f = 0$ almost everywhere.

Integrability of $x^{-a}\log(x)$

Aggregating and differentiating under integral sign

Functions involving expectations - The dominated/monotone convergence theorem

Is $L^\infty$ a subset of $L^p$ for finite $p$?

Moment of measure for Dirac disintegration

Substitution rule for dirac measure

How to prove that $\mathbf{E}\eta = \int_{0}^{\infty}\mathbf{P}(\{\eta > z\})dz$ for arbitrary non-negative random variable?

If $f\in L^1([0,\infty ))$ then $\lim_{n\to \infty}\frac{1}{n}\int_{[0,n]}xf(x)dx=0$

$L^1$ function that is not $L^p$ for $p > 1$.

Lesbesgue theorem for differentiation of indefinite integrals

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