List questions from lebesgue-integral

Published on 11 Apr 2026 - 19:10

127

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Why is the Lebesgue integral not affected by the presentation of a simple function?

Published on 12 Apr 2026 - 12:46

261

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Rigorous definition of characteristic function of random variable as Lebesgue integral

Published on 09 Apr 2026 - 21:49

1.1k

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Integral of $L1$ function against compactly supported smooth function:

Published on 11 Apr 2026 - 9:22

77

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If $f$ is an $L_1$ function, how to prove this integration identity by substitution?

Published on 15 Apr 2026 - 3:58

30

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show that the integral exists if and only if λ ((A ∪ B)^c ∩ J) = 0

Published on 13 Apr 2026 - 13:48

525

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L2 Norm Inequality

Published on 10 May 2026 - 13:22

112

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Limit of Cosine Integral

Published on 11 May 2026 - 2:33

396

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Riemann-Lebesgue lemma for arbitrary simple function

Published on 14 Apr 2026 - 10:13

200

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Extending continuous functions from almost everywhere to everywhere

Published on 10 May 2026 - 16:48

125

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Exercise on a sequence of funcions $f_n\rightarrow f$ and Lebesgue Theorem.

Published on 13 Apr 2026 - 14:37

385

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Range of an integral operator

Published on 10 May 2026 - 18:02

99

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Prove $\lambda(G)=1/(a-1)$ where $G=\{(x,y)|1<x \wedge 0<y<x^{-a} \}$ with $a>1$

Published on 15 Apr 2026 - 23:22

55

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Equivalent condition of $f$ to be $L^2$

Published on 10 May 2026 - 17:38

781

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Weird use of Glasser's Master Theorem

Published on 11 Apr 2026 - 14:17

List Question

A question on relating Riemann-Stieltjes integral and Lebesgue integral

Why is the Lebesgue integral not affected by the presentation of a simple function?

Rigorous definition of characteristic function of random variable as Lebesgue integral

Integral of $L1$ function against compactly supported smooth function:

If $f$ is an $L_1$ function, how to prove this integration identity by substitution?

show that the integral exists if and only if λ ((A ∪ B)^c ∩ J) = 0

L2 Norm Inequality

Limit of Cosine Integral

Riemann-Lebesgue lemma for arbitrary simple function

Extending continuous functions from almost everywhere to everywhere

Exercise on a sequence of funcions $f_n\rightarrow f$ and Lebesgue Theorem.

Range of an integral operator

Prove $\lambda(G)=1/(a-1)$ where $G=\{(x,y)|1<x \wedge 0<y<x^{-a} \}$ with $a>1$

Equivalent condition of $f$ to be $L^2$

Weird use of Glasser's Master Theorem

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