List questions from lebesgue-integral

Published on 13 Apr 2026 - 4:30

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Combinations of integrable functions

Published on 11 Apr 2026 - 1:43

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$f$ absolutely continuous and $f'\in L^3[0,1]$, which values of $\alpha $ does $\lim_{x\rightarrow 0^+} x^{-\alpha}f(x)=0$?

Published on 14 Apr 2026 - 22:26

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List all the possible values for $\int_{\mathbb{R}}\sup_{k\in\mathbb{N}}f_k(x)dx$ under these conditions...

Published on 17 Apr 2026 - 2:31

196

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Almost everywhere pointwise convergence

Published on 13 Apr 2026 - 17:08

75

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Lebesgue dominated convergence counterexample

Published on 13 Apr 2026 - 8:27

137

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Integrable function $f$ such that $\int_I f(x)dx=0$ for intervals of arbitrarily small length.

Published on 16 Apr 2026 - 6:11

33

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Convergence of integrals of function sequences evaluated by inequalities.

Published on 13 Apr 2026 - 0:03

311

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Prove that $f$ is Lebesgue integrable on $E$ if and only if $\sum_{n=0}^\infty 2^nm(\{x\in E:f(x)\geq2^n\})<\infty$

Published on 15 Apr 2026 - 23:27

439

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Lebesgue measure of a subset [$0,1$]

Published on 13 Apr 2026 - 16:11

94

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Convergence in $p$th mean does not imply convergence in mean.

Published on 04 May 2026 - 21:21

122

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Show that $f$ is measurable with respect to $L$.

Published on 14 Apr 2026 - 8:26

136

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Problem with showing $\lim_{n\rightarrow \infty} \int_A \cos(nxy) \, d\lambda_2=0$

Published on 15 Apr 2026 - 19:45

97

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Is the function $f = \sum_{n=0}^{\infty} 2^{-n}\chi_{[n,n+1)}$ Lebesgue integrable on $\mathbb{R}$?

Published on 13 Apr 2026 - 17:26

203

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Find $\lim inf A_n$ and $\lim sup A_n$

Published on 16 Apr 2026 - 12:07

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Riemann Stieltjes integral definition and implications

Combinations of integrable functions

$f$ absolutely continuous and $f'\in L^3[0,1]$, which values of $\alpha $ does $\lim_{x\rightarrow 0^+} x^{-\alpha}f(x)=0$?

List all the possible values for $\int_{\mathbb{R}}\sup_{k\in\mathbb{N}}f_k(x)dx$ under these conditions...

Almost everywhere pointwise convergence

Lebesgue dominated convergence counterexample

Integrable function $f$ such that $\int_I f(x)dx=0$ for intervals of arbitrarily small length.

Convergence of integrals of function sequences evaluated by inequalities.

Prove that $f$ is Lebesgue integrable on $E$ if and only if $\sum_{n=0}^\infty 2^nm(\{x\in E:f(x)\geq2^n\})<\infty$

Lebesgue measure of a subset [$0,1$]

Convergence in $p$th mean does not imply convergence in mean.

Show that $f$ is measurable with respect to $L$.

Problem with showing $\lim_{n\rightarrow \infty} \int_A \cos(nxy) \, d\lambda_2=0$

Is the function $f = \sum_{n=0}^{\infty} 2^{-n}\chi_{[n,n+1)}$ Lebesgue integrable on $\mathbb{R}$?

Find $\lim inf A_n$ and $\lim sup A_n$

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