List questions from lebesgue-integral

Published on 14 Apr 2023 - 23:19

70

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Differentiating under the integral sign in $n$ variables to show $\partial^{\alpha}(fg)=f\partial^{\alpha}g$

Published on 01 Apr 2026 - 12:31

134

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Application of Sobolev's inequality

Published on 11 Apr 2026 - 17:38

62

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Integrating term-by-term in a Lebesgue integral

Published on 11 Apr 2026 - 3:57

42

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Restricting σ-algebra

Published on 29 Mar 2026 - 21:49

72

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Dominated Convergence Theorem on an integral

Published on 09 Apr 2026 - 12:18

101

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Lebesgue measure and Intermediate Value Theorem

Published on 10 Apr 2026 - 16:31

58

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$\int_{0}^{x} f(z)dz =0$ for all $x \in A$ where $\lambda([0,\infty) \setminus A) =0$, i.e. a.e., implies $f$ is zero a.e.

Published on 19 Apr 2023 - 8:13

248

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$g(z) = \int_0^1 f(t)e^{tz^2} dt$ defines an entire function

Published on 28 Mar 2026 - 3:30

70

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Evaluate the integral $\lim_{n\to\infty}\int_0^1{\frac{nx\cdot \sin(x)}{1 + (nx)^a}}dx$

Published on 20 Apr 2023 - 2:50

44

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Find the series $\{a_i\}_{i=-\infty}^{+\infty}$ - Linear system course

Published on 20 Apr 2023 - 17:51

27

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what is lebesgue integral of f(x) = n if 0<x<1/n and f(x)=0 otherwise

Published on 23 Apr 2023 - 9:52

77

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Find a function $\psi$ s.t. $\forall f\in\mathcal{F},f\le\psi$ a.e. , where $\mathcal{F}$ is a given subset in $L^{1}(\mathbb{R})$

Published on 09 Apr 2026 - 9:26

158

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Show $\lim_{n \to \infty}|\cos nx|^{1/n}=1$ almost everywhere

Published on 24 Apr 2023 - 1:41

36

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Investigate and if possible determine the value of the integrals

Published on 24 Apr 2023 - 12:53

List Question

Isomorphism of the measure algebra on $[0, 1]$

Differentiating under the integral sign in $n$ variables to show $\partial^{\alpha}(fg)=f\partial^{\alpha}g$

Application of Sobolev's inequality

Integrating term-by-term in a Lebesgue integral

Restricting σ-algebra

Dominated Convergence Theorem on an integral

Lebesgue measure and Intermediate Value Theorem

$\int_{0}^{x} f(z)dz =0$ for all $x \in A$ where $\lambda([0,\infty) \setminus A) =0$, i.e. a.e., implies $f$ is zero a.e.

$g(z) = \int_0^1 f(t)e^{tz^2} dt$ defines an entire function

Evaluate the integral $\lim_{n\to\infty}\int_0^1{\frac{nx\cdot \sin(x)}{1 + (nx)^a}}dx$

Find the series $\{a_i\}_{i=-\infty}^{+\infty}$ - Linear system course

what is lebesgue integral of f(x) = n if 0<x<1/n and f(x)=0 otherwise

Find a function $\psi$ s.t. $\forall f\in\mathcal{F},f\le\psi$ a.e. , where $\mathcal{F}$ is a given subset in $L^{1}(\mathbb{R})$

Show $\lim_{n \to \infty}|\cos nx|^{1/n}=1$ almost everywhere

Investigate and if possible determine the value of the integrals

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