List questions from measure-theory

Published on 13 Apr 2026 - 8:48

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Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

Published on 13 Apr 2026 - 20:09

601

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$n\chi_{[0, 1/n]}$ converges pointwise

Published on 09 Apr 2026 - 17:12

416

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Prove that if the outer measure of a set $E$ is the supremum of the measure of closed bdd sets, then $E$ is measurable.

Published on 16 Apr 2026 - 7:37

958

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$f = g$ almost everywhere implies $f =g$ for any continuous function $f$ and $g$.

Published on 14 Apr 2026 - 2:21

56

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Convergence of product of random variables

Published on 13 Apr 2026 - 5:33

171

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$\phi(t) = \int f(t,\omega)d\mu(\omega)$ is everywhere differentiable and moreover, $\phi^/(t)=\int(t,\omega)d\mu(\omega)$

Published on 17 Apr 2026 - 2:38

69

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Show $s(f) = \int_{\_a}^b f $

Published on 16 Apr 2026 - 21:11

142

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Sensitivity of Lebesgue measure of level sets

Published on 10 Apr 2026 - 10:13

1.1k

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Definition of predictable process

Published on 09 Apr 2026 - 0:09

80

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Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

Published on 17 Apr 2026 - 4:42

73

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Find the value of $\lim_{n \rightarrow \infty} \int_{0}^{1+ \frac{1}{n}} n \cdot \log(1+ \frac{x^2}{n}) dx$

Published on 17 Apr 2026 - 12:29

57

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Soft Question - Motivation of the Pettis Integral

Published on 10 Apr 2026 - 4:11

296

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Fubini's theorem: Two dimensional Lebesgue integration (Bivariate uniform distribution probability calculation)

Published on 11 Apr 2026 - 13:02

293

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How to apply the Lebesgue Dominated Convergence Theorem

Published on 10 Apr 2026 - 0:11

List Question

Notation Question Measure Theory

Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

$n\chi_{[0, 1/n]}$ converges pointwise

Prove that if the outer measure of a set $E$ is the supremum of the measure of closed bdd sets, then $E$ is measurable.

$f = g$ almost everywhere implies $f =g$ for any continuous function $f$ and $g$.

Convergence of product of random variables

$\phi(t) = \int f(t,\omega)d\mu(\omega)$ is everywhere differentiable and moreover, $\phi^/(t)=\int(t,\omega)d\mu(\omega)$

Show $s(f) = \int_{\_a}^b f $

Sensitivity of Lebesgue measure of level sets

Definition of predictable process

Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

Find the value of $\lim_{n \rightarrow \infty} \int_{0}^{1+ \frac{1}{n}} n \cdot \log(1+ \frac{x^2}{n}) dx$

Soft Question - Motivation of the Pettis Integral

Fubini's theorem: Two dimensional Lebesgue integration (Bivariate uniform distribution probability calculation)

How to apply the Lebesgue Dominated Convergence Theorem

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