List questions from lebesgue-integral

Published on 12 Apr 2026 - 19:24

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Is this family of functions uniformly integrable over $[0,1]$

Published on 11 Apr 2026 - 2:53

976

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Interchanging Expectation and Derivative

Published on 14 Apr 2026 - 0:25

71

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Can Lebesgue Dominated Convergence always be used?

Published on 12 Apr 2026 - 2:03

1.9k

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Difference between $d\mu(x)$ and $\mu(dx)$

Published on 12 Apr 2026 - 23:02

64

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$f \in L^1(\mathbb{R})$ implies there exists $a \in \mathbb{R}$ with $\int_{(-\infty, a]} f = \int_{[a, \infty)} f$

Published on 17 Apr 2026 - 1:26

427

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How to apply Fubini's theorem?

Published on 09 Apr 2026 - 7:19

86

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Evaluation of $\int_{[0,\infty)}\biggl(\int_{[0,\infty)}2x\sqrt{y}e^{-x^2\sqrt{y}-y}dy\biggl)dx$.

Published on 15 Apr 2026 - 22:14

93

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How to use Cavalieri?

Published on 08 Apr 2026 - 0:14

32

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$L^1$ approximation by a slightly "displaced" copy

Published on 26 Apr 2026 - 13:17

461

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Questions on measurable sets

Published on 11 Apr 2026 - 3:56

86

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Lebesgue integral of $-\frac{1}{n}$

Published on 11 Apr 2026 - 16:26

93

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When we can permute between the integral and convex hull?

Published on 11 Apr 2026 - 7:12

1.6k

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Does existence of the second weak derivative of $f\in L^2$ imply existence of the first?

Published on 28 Mar 2026 - 1:26

1.4k

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Proofs related to chi-squared distribution for k degrees of freedom

Published on 14 Apr 2026 - 7:47

List Question

Calculate the next limit. Lebesgue integral.

Is this family of functions uniformly integrable over $[0,1]$

Interchanging Expectation and Derivative

Can Lebesgue Dominated Convergence always be used?

Difference between $d\mu(x)$ and $\mu(dx)$

$f \in L^1(\mathbb{R})$ implies there exists $a \in \mathbb{R}$ with $\int_{(-\infty, a]} f = \int_{[a, \infty)} f$

How to apply Fubini's theorem?

Evaluation of $\int_{[0,\infty)}\biggl(\int_{[0,\infty)}2x\sqrt{y}e^{-x^2\sqrt{y}-y}dy\biggl)dx$.

How to use Cavalieri?

$L^1$ approximation by a slightly "displaced" copy

Questions on measurable sets

Lebesgue integral of $-\frac{1}{n}$

When we can permute between the integral and convex hull?

Does existence of the second weak derivative of $f\in L^2$ imply existence of the first?

Proofs related to chi-squared distribution for k degrees of freedom

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