List questions from lebesgue-integral

Published on 11 Apr 2026 - 13:25

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Fubini-Tonelli theorem and absolutely Lebesuge integrable functions

Published on 11 Apr 2026 - 6:40

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$\left\|f\right\|_{L^1(μ_1)}<∞$ $μ_2$-a.e.,$\left\|f\right\|_{L^1(μ_2)}<∞$ $μ_1$-a.e. $⇒$ $\left\|f\right\|_{L^1(μ_1\otimesμ_2)}<∞$

Published on 22 Apr 2026 - 3:50

142

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Prove that $\lim_n \int_{\Bbb R} \frac{\sin(n^2 x^5)}{n^2 x^4} \chi_{(0,n]} d\lambda(x) = 0$

Published on 17 Apr 2026 - 6:17

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Fubini's Theorem and expectation of random variables

Published on 13 Apr 2026 - 1:24

42

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Prove $F$ is in $L^1$

Published on 22 Apr 2026 - 3:46

1k

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Helmholtz theorem

Published on 26 Apr 2026 - 0:48

56

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Let $f \in L^{1}([0,1])$ be a real valued function. Prove the following

Published on 22 Apr 2026 - 3:48

182

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Measure Theory and $L^{p}$ spaces

Published on 22 Apr 2026 - 3:42

162

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Does $\int f(s) ds = \int g(s) ds \not =0$ imply $f(s)=g(s)$?

Published on 16 Apr 2026 - 19:57

216

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How to integrate with a matrix in the measure?

Published on 26 Mar 2026 - 6:05

327

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Prove $\lim_{n \rightarrow \infty} n \int_{\frac{1}{n}}^{1} \frac{\cos(x+\frac{1}{n})-\cos(x)}{x^{\frac{3}{2}}}dx$ exists.

Published on 16 Apr 2026 - 4:35

65

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A limit of integral

Published on 11 Apr 2026 - 7:17

69

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Continuous map from $L^r(\Omega)$ to $L^s(\Omega)$.

Published on 12 Apr 2026 - 3:46

1.4k

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Counting measure on the power set sigma-algebra for the natural numbers

Published on 11 Apr 2026 - 23:03

List Question

Application of Leibniz rule for Lebesgue integral

Fubini-Tonelli theorem and absolutely Lebesuge integrable functions

$\left\|f\right\|_{L^1(μ_1)}<∞$ $μ_2$-a.e.,$\left\|f\right\|_{L^1(μ_2)}<∞$ $μ_1$-a.e. $⇒$ $\left\|f\right\|_{L^1(μ_1\otimesμ_2)}<∞$

Prove that $\lim_n \int_{\Bbb R} \frac{\sin(n^2 x^5)}{n^2 x^4} \chi_{(0,n]} d\lambda(x) = 0$

Fubini's Theorem and expectation of random variables

Prove $F$ is in $L^1$

Helmholtz theorem

Let $f \in L^{1}([0,1])$ be a real valued function. Prove the following

Measure Theory and $L^{p}$ spaces

Does $\int f(s) ds = \int g(s) ds \not =0$ imply $f(s)=g(s)$?

How to integrate with a matrix in the measure?

Prove $\lim_{n \rightarrow \infty} n \int_{\frac{1}{n}}^{1} \frac{\cos(x+\frac{1}{n})-\cos(x)}{x^{\frac{3}{2}}}dx$ exists.

A limit of integral

Continuous map from $L^r(\Omega)$ to $L^s(\Omega)$.

Counting measure on the power set sigma-algebra for the natural numbers

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