List questions from lebesgue-integral

Published on 15 Apr 2026 - 9:32

147

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Equivalent definition of locally integrable function

Published on 10 Apr 2026 - 16:14

942

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If $a_n=\int_n^{n+1} f,$ is it true that $f$ is Lebesgue integrable over $[1,\infty)$ if and only if the series $\sum_{n=1}^\infty a_n$ converges?

Published on 16 Apr 2026 - 12:58

94

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Showing that a $L^2$-norm is positive

Published on 11 Apr 2026 - 16:28

68

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How to show that $ \int_1^{+\infty} \frac{\sin \frac{1}{x}}{x^a} \mathrm{d}x$ is not integrable?

Published on 15 Apr 2026 - 4:08

59

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Approximation by a radial function

Published on 14 Apr 2026 - 15:15

224

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Prove that $F(z)=\int_Xf(x,z)d\mu(x) $ is holomorphic

Published on 15 Apr 2026 - 11:38

263

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Regularity of a function

Published on 12 Apr 2026 - 5:36

62

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Determine for which $\alpha \in\mathbb{R}$ one has $f\in L^p(\mathbb{R})$.

Published on 14 Apr 2026 - 1:57

52

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Show the described set is a subset of $L^p(\mu)$

Published on 30 Apr 2026 - 9:46

64

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Integrability of a limit of functions

Published on 30 Apr 2026 - 9:46

1.7k

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Are there any unsolved Problems in Theory of Integration?

Published on 26 Mar 2026 - 9:40

919

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Differentiation of the Newtonian potential of a function (Sandro Salsa's PDE book)

Published on 12 Apr 2026 - 4:00

188

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not lebesgue integrable function

Published on 12 Apr 2026 - 6:02

1.3k

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Show that $\lim_{k\to\infty} \int_0^1 f(x) \sin(kx) \, dx = 0$

Published on 14 Apr 2026 - 18:44

List Question

Prove that $\int_A f = \int_E f\chi_A$ using definition of Lebesgue integral

Equivalent definition of locally integrable function

If $a_n=\int_n^{n+1} f,$ is it true that $f$ is Lebesgue integrable over $[1,\infty)$ if and only if the series $\sum_{n=1}^\infty a_n$ converges?

Showing that a $L^2$-norm is positive

How to show that $ \int_1^{+\infty} \frac{\sin \frac{1}{x}}{x^a} \mathrm{d}x$ is not integrable?

Approximation by a radial function

Prove that $F(z)=\int_Xf(x,z)d\mu(x) $ is holomorphic

Regularity of a function

Determine for which $\alpha \in\mathbb{R}$ one has $f\in L^p(\mathbb{R})$.

Show the described set is a subset of $L^p(\mu)$

Integrability of a limit of functions

Are there any unsolved Problems in Theory of Integration?

Differentiation of the Newtonian potential of a function (Sandro Salsa's PDE book)

not lebesgue integrable function

Show that $\lim_{k\to\infty} \int_0^1 f(x) \sin(kx) \, dx = 0$

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