List questions from lebesgue-integral

Published on 10 May 2019 - 13:01

38

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Showing the equality of two integrals

Published on 10 May 2019 - 23:53

225

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How do we need to apply the martingale convergence theorem here?

Published on 25 Mar 2026 - 20:35

772

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When is $\int_0^1 \int_0^1 \frac{f(x) - f(y)}{x-y} \, \text{d} x \, \text{d} y = 2 \int_0^1 f(t) \log\left(\frac{t}{1-t}\right) \, \mathrm{d} t$?

Published on 11 May 2019 - 23:11

403

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if and only if condition for a function to be a Lebesgue Integrable.

Published on 12 May 2019 - 5:53

135

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Show that $\int_\mathbb{R^n} F(|g(x)|) dx = - \int_0^{\infty} F(\alpha) d \lambda(\alpha) = \int_0^{\infty} F'(\alpha) \lambda(\alpha) d\alpha$

Published on 12 May 2019 - 7:01

58

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Convergence of integral with compact support

Published on 12 May 2019 - 8:00

75

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Sequence of measures in L-p Spaces

Published on 13 May 2019 - 10:41

71

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A limit of an integral of a quotient related to fractional Sobolev space

Published on 14 May 2019 - 0:23

262

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Prove that $f$ is not Lebesgue integrable

Published on 14 May 2019 - 3:23

1.5k

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Give an example of strict inequality in Fatou's Lemma

Published on 14 May 2019 - 5:17

52

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Let $(f_n)$ be a sequence in $M^+(\mathbb{R})$ proove that $ \displaystyle{\int \sum_{n=1}^{\infty}f_n = \sum_{n=1}^{\infty}\int f_n}$

Published on 14 May 2019 - 6:36

25

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Reweighting preserves positive average

Published on 25 Mar 2026 - 18:52

30

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Motion of a particle defined via Lebesgue integral

Published on 15 May 2019 - 17:15

72

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Evaluate $\lim_{n \to \infty}\int_{0}^{1}\frac{n+\cos^n(e^x)}{4n+x^4} dx$

Published on 28 Mar 2026 - 4:53

List Question

Rewriting expectation (Lebesgue)

Showing the equality of two integrals

How do we need to apply the martingale convergence theorem here?

When is $\int_0^1 \int_0^1 \frac{f(x) - f(y)}{x-y} \, \text{d} x \, \text{d} y = 2 \int_0^1 f(t) \log\left(\frac{t}{1-t}\right) \, \mathrm{d} t$?

if and only if condition for a function to be a Lebesgue Integrable.

Show that $\int_\mathbb{R^n} F(|g(x)|) dx = - \int_0^{\infty} F(\alpha) d \lambda(\alpha) = \int_0^{\infty} F'(\alpha) \lambda(\alpha) d\alpha$

Convergence of integral with compact support

Sequence of measures in L-p Spaces

A limit of an integral of a quotient related to fractional Sobolev space

Prove that $f$ is not Lebesgue integrable

Give an example of strict inequality in Fatou's Lemma

Let $(f_n)$ be a sequence in $M^+(\mathbb{R})$ proove that $ \displaystyle{\int \sum_{n=1}^{\infty}f_n = \sum_{n=1}^{\infty}\int f_n}$

Reweighting preserves positive average

Motion of a particle defined via Lebesgue integral

Evaluate $\lim_{n \to \infty}\int_{0}^{1}\frac{n+\cos^n(e^x)}{4n+x^4} dx$

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