List questions from lebesgue-integral

Published on 10 Feb 2017 - 21:29

2.3k

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Showing that the Lebesgue-Stieltjes measure is absolutely continuous with respect to Lebesgue measure (and one more thing).

Published on 11 Feb 2017 - 2:52

44

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How to evaluate $\int_A x^2 + y^2 d\lambda^2(x, y)$ with the change-of-variables formula?

Published on 29 Mar 2026 - 7:38

131

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Proof that the limit of a particular sequence of Lebesgue integrals equals zero.

Published on 11 Feb 2017 - 12:26

781

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Lebesgue-Stieltjes measure absolutely continous with respect to Lebesgue measure.

Published on 09 Apr 2026 - 2:54

1.8k

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Showing that $f'$ is the Radon-Nikodym derivative of $\lambda_f$

Published on 11 Feb 2017 - 13:50

618

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Limit of integrals using the dominated convergence theorem

Published on 12 Feb 2017 - 10:08

350

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$E(X)=\int_{0}^{\infty}P(X>y)dy$ for non-negative r.v. $X$

Published on 12 Feb 2017 - 15:24

323

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Compute $\lim\limits_{n\to \infty} \int_{0}^{\infty} \exp(-x)(\cos(x))^n dx$

Published on 13 Feb 2017 - 16:28

375

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Is $f_n(x)=\chi_{[n,n+1]}$ tight?

Published on 13 Feb 2017 - 23:20

99

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Compute $\lim_{n\to \infty} \int_{[0, \pi/4]} \text{sin}(nx)\text{log}(1+x^n)\,d\lambda(x)$

Published on 14 Feb 2017 - 15:47

336

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Riesz potential-inequality

Published on 09 Apr 2026 - 1:14

309

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$\lim_{n \to \infty} P(A_n) = 0$ implies $\lim_{n\to\infty}\int_{A_n}{X}dP = 0$

Published on 14 Feb 2017 - 22:40

76

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Application of change of variables in $\mathbb{R}^2$

Published on 08 Apr 2026 - 21:45

577

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Is the sequence of functions $f_n=\chi_{[n,n+1]}$ uniformly integrable?

Published on 26 Mar 2026 - 8:03

List Question

How show that this set is closed?

Showing that the Lebesgue-Stieltjes measure is absolutely continuous with respect to Lebesgue measure (and one more thing).

How to evaluate $\int_A x^2 + y^2 d\lambda^2(x, y)$ with the change-of-variables formula?

Proof that the limit of a particular sequence of Lebesgue integrals equals zero.

Lebesgue-Stieltjes measure absolutely continous with respect to Lebesgue measure.

Showing that $f'$ is the Radon-Nikodym derivative of $\lambda_f$

Limit of integrals using the dominated convergence theorem

$E(X)=\int_{0}^{\infty}P(X>y)dy$ for non-negative r.v. $X$

Compute $\lim\limits_{n\to \infty} \int_{0}^{\infty} \exp(-x)(\cos(x))^n dx$

Is $f_n(x)=\chi_{[n,n+1]}$ tight?

Compute $\lim_{n\to \infty} \int_{[0, \pi/4]} \text{sin}(nx)\text{log}(1+x^n)\,d\lambda(x)$

Riesz potential-inequality

$\lim_{n \to \infty} P(A_n) = 0$ implies $\lim_{n\to\infty}\int_{A_n}{X}dP = 0$

Application of change of variables in $\mathbb{R}^2$

Is the sequence of functions $f_n=\chi_{[n,n+1]}$ uniformly integrable?

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