Question

Radon-Nikodym derivatives. Royden, Problem 33.

score 151 · Answer 1 · 2026-04-09 09:30:43

151

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Radon-Nikodym derivatives. Royden, Problem 33.

Published on 09 Apr 2026 - 9:30

score 228 · Answer 2 · 2026-04-16 00:28:18

228

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If $(Ω,A,\text P)$ is a non-atomic prob. space and $μ$ is a prob. measure on a Borel space there is a variable on $(Ω,A,\text P)$ with law $μ$

Published on 16 Apr 2026 - 0:28

score 571 · Answer 3 · 2026-05-10 18:03:52

571

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$\int_A f = \int_A g \implies f = g$ a.e.

Published on 10 May 2026 - 18:03

score 227 · Answer 4 · 2026-04-13 14:13:38

227

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Measure of a compact subset of $\mathbb{R}^d$

Published on 13 Apr 2026 - 14:13

score 172 · Answer 5 · 2026-05-11 06:34:21

172

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$\liminf E_{n_0+n} = \liminf\limits E_{n}$ and $\limsup E_{n_0+n} = \limsup E_{n}$ where $E_n$ is a decreasing sequence?

Published on 11 May 2026 - 6:34

score 66 · Answer 6 · 2026-04-14 17:10:07

Please help me to show analytically that for A $\subseteq$ Ω, the following collection of sets F ={∅,Ω,A,Ac}, is a sigma-algebra of subsets of Ω.

score 62 · Answer 7 · 2026-04-15 15:51:40

62

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Sigmas Problem ΣΣ i^2

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score 82 · Answer 8 · 2026-04-11 22:53:06

82

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Hausdorff measure and angle of a regular simplex/tetrahedron

Published on 11 Apr 2026 - 22:53

score 47 · Answer 9 · 2026-04-17 08:34:46

47

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Why is $\frac{x^n}{x^3+x^4}\chi_{[0,1[} \in \mathcal{L}^1$

Published on 17 Apr 2026 - 8:34

score 264 · Answer 10 · 2026-04-10 01:30:47

264

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Kolmogorov extension theorem for measures on the space of continuous functions

Published on 10 Apr 2026 - 1:30

score 714 · Answer 11 · 2026-05-10 15:24:14

714

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$f$ measurable iff $f^2$ measurable and $\{f > 0\}$ measurable

Published on 10 May 2026 - 15:24

score 276 · Answer 12 · 2026-04-16 23:26:29

276

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$f \circ | \cdot |$ Lebesgue Integrable $\iff$ g is Lebesgue Integrable

Published on 16 Apr 2026 - 23:26

score 124 · Answer 13 · 2026-04-17 05:23:01

124

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Prove $\int_{\mathbb R^{d}}f(|y|)d\lambda^{d}(y)=C_{d}\int_{[0,\infty[}r^{d-1}f(r)d\lambda^{1}(r)$

Published on 17 Apr 2026 - 5:23

score 245 · Answer 14 · 2026-04-14 02:48:20

245

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Convergence in $L^1$ implies Convergence in measure using Chebyshev's Inequality

Published on 14 Apr 2026 - 2:48

score 322 · Answer 15 · 2026-04-08 17:17:22

322

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Measure theory integral

Published on 08 Apr 2026 - 17:17

List Question

Radon-Nikodym derivatives. Royden, Problem 33.

If $(Ω,A,\text P)$ is a non-atomic prob. space and $μ$ is a prob. measure on a Borel space there is a variable on $(Ω,A,\text P)$ with law $μ$

$\int_A f = \int_A g \implies f = g$ a.e.

Measure of a compact subset of $\mathbb{R}^d$

$\liminf E_{n_0+n} = \liminf\limits E_{n}$ and $\limsup E_{n_0+n} = \limsup E_{n}$ where $E_n$ is a decreasing sequence?

Please help me to show analytically that for A $\subseteq$ Ω, the following collection of sets F ={∅,Ω,A,Ac}, is a sigma-algebra of subsets of Ω.

Sigmas Problem ΣΣ i^2

Hausdorff measure and angle of a regular simplex/tetrahedron

Why is $\frac{x^n}{x^3+x^4}\chi_{[0,1[} \in \mathcal{L}^1$

Kolmogorov extension theorem for measures on the space of continuous functions

$f$ measurable iff $f^2$ measurable and $\{f > 0\}$ measurable

$f \circ | \cdot |$ Lebesgue Integrable $\iff$ g is Lebesgue Integrable

Prove $\int_{\mathbb R^{d}}f(|y|)d\lambda^{d}(y)=C_{d}\int_{[0,\infty[}r^{d-1}f(r)d\lambda^{1}(r)$

Convergence in $L^1$ implies Convergence in measure using Chebyshev's Inequality

Measure theory integral

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