Question

Understanding Proposition 3.9 Folland Part 2 (Radon-Nikodym Derivative)

score 513 · Answer 1 · 2026-04-09 07:31:19

513

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Understanding Proposition 3.9 Folland Part 2 (Radon-Nikodym Derivative)

Published on 09 Apr 2026 - 7:31

score 61 · Answer 2 · 2026-04-15 03:09:25

61

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Product measure : difference between $\mathcal M\times \mathcal M$ and $\{A\times B\mid A,B\in \mathcal M\}$

Published on 15 Apr 2026 - 3:09

score 58 · Answer 3 · 2026-04-15 21:53:22

If $A\times B$ is an element of a product $\sigma$-algebra $\mathcal A\times\mathcal B$ then do we have $A\in\mathcal A$ and $B\in\mathcal B$?

score 6k · Answer 4 · 2026-04-09 09:25:05

6k

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should I learn measure theory before learning probability?

Published on 09 Apr 2026 - 9:25

score 408 · Answer 5 · 2026-04-14 00:59:47

408

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Show that the set $D_b$ is a Dynkin-System

Published on 14 Apr 2026 - 0:59

score 505 · Answer 6 · 2026-04-16 06:44:14

505

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$\mu$ is $\sigma$-finite $\iff \exists$ function $f \in \mathcal{L}^{1}(\mu)$ with $f(x)>0$ for all $x \in X$

Published on 16 Apr 2026 - 6:44

score 217 · Answer 7 · 2026-05-10 14:38:15

217

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$\lambda$-almost-everywhere convergence implied by lim$\lambda (${$x \in E : | f_n(x) - f(x) | > \epsilon$}$) = 0$

Published on 10 May 2026 - 14:38

score 76 · Answer 8 · 2026-05-01 04:20:22

76

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Computing iterated integrals over positive integers (question about stack exchange solution)

Published on 01 May 2026 - 4:20

score 78 · Answer 9 · 2026-04-16 00:30:42

78

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Find $\lim_{n\to \infty} \int_{\mathbb R}\frac{n \log^{4}(x)}{n+nx+x^2}\chi_{[0,\infty[}d\lambda(x)$

Published on 16 Apr 2026 - 0:30

score 464 · Answer 10 · 2026-05-13 11:01:18

464

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Equality of finite signed measures by showing that the integrals of every bounded continuous function coincide

Published on 13 May 2026 - 11:01

score 235 · Answer 11 · 2026-04-12 08:12:39

235

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Convergence and Measure

Published on 12 Apr 2026 - 8:12

score 1.8k · Answer 12 · 2026-04-15 08:38:30

1.8k

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Prove that Geometric mean is less than Arithmetic mean using Jensen's inequality

Published on 15 Apr 2026 - 8:38

score 1k · Answer 13 · 2026-04-13 08:49:19

1k

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a.e. point wise convergence on finite measured set implies convergence in measure

Published on 13 Apr 2026 - 8:49

score 177 · Answer 14 · 2026-04-11 18:13:58

177

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Lebesgue measure (unit square/integral)

Published on 11 Apr 2026 - 18:13

score 45 · Answer 15 · 2026-04-16 09:58:25

45

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Find $\lim_{n\to\infty}\int_{[0,\infty[}\frac{x}{\sqrt[n]{1+x^{3n}}}$

Published on 16 Apr 2026 - 9:58

List Question

Understanding Proposition 3.9 Folland Part 2 (Radon-Nikodym Derivative)

Product measure : difference between $\mathcal M\times \mathcal M$ and $\{A\times B\mid A,B\in \mathcal M\}$

If $A\times B$ is an element of a product $\sigma$-algebra $\mathcal A\times\mathcal B$ then do we have $A\in\mathcal A$ and $B\in\mathcal B$?

should I learn measure theory before learning probability?

Show that the set $D_b$ is a Dynkin-System

$\mu$ is $\sigma$-finite $\iff \exists$ function $f \in \mathcal{L}^{1}(\mu)$ with $f(x)>0$ for all $x \in X$

$\lambda$-almost-everywhere convergence implied by lim$\lambda (${$x \in E : | f_n(x) - f(x) | > \epsilon$}$) = 0$

Computing iterated integrals over positive integers (question about stack exchange solution)

Find $\lim_{n\to \infty} \int_{\mathbb R}\frac{n \log^{4}(x)}{n+nx+x^2}\chi_{[0,\infty[}d\lambda(x)$

Equality of finite signed measures by showing that the integrals of every bounded continuous function coincide

Convergence and Measure

Prove that Geometric mean is less than Arithmetic mean using Jensen's inequality

a.e. point wise convergence on finite measured set implies convergence in measure

Lebesgue measure (unit square/integral)

Find $\lim_{n\to\infty}\int_{[0,\infty[}\frac{x}{\sqrt[n]{1+x^{3n}}}$

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