Question

Proving the Borel-Cantelli Lemma

score 1.1k · Answer 1 · 2026-05-05 21:45:31

1.1k

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Proving the Borel-Cantelli Lemma

Published on 05 May 2026 - 21:45

score 122 · Answer 2 · 2026-04-14 07:58:38

122

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Is the set of continuous functions measurable?

Published on 14 Apr 2026 - 7:58

score 201 · Answer 3 · 2026-05-10 20:53:07

201

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Is the set of Borel measurable transformations the closure of continuous functions under pointwise limits?

Published on 10 May 2026 - 20:53

score 75 · Answer 4 · 2026-05-16 21:17:05

75

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Comparing $\sigma$ algebras with topologies

Published on 16 May 2026 - 21:17

score 191 · Answer 5 · 2026-05-05 21:45:03

191

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Problem 4 part (a) from Stein's Real Analysis

Published on 05 May 2026 - 21:45

score 260 · Answer 6 · 2026-05-16 21:16:59

260

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Prove $h(y) = \int_{\mathbb{R}} f(x,y) dx$ is continuous if $f(x,y)$ is continuous for every fixed $x$ and $f(x,y)$ is integrable for every fixed $y$.

Published on 16 May 2026 - 21:16

score 39 · Answer 7 · 2026-04-15 21:14:28

Is $\mu_X\otimes \mu_Y(A\times B)=\int_A \mu_Y(B^x)\mu_X(dx)$ hold if $X$ and $Y$ are not independents random variables?

score 1.1k · Answer 8 · 2026-05-06 02:41:55

1.1k

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The set at which a function's oscillation is at least $\epsilon$ is closed

Published on 06 May 2026 - 2:41

score 162 · Answer 9 · 2026-04-08 05:15:00

162

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Relationship between a parametric family of distributions and the measure of probability

Published on 08 Apr 2026 - 5:15

score 2.3k · Answer 10 · 2026-05-06 02:43:00

2.3k

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$f$ is Riemann integrable if the set of discontinuities is measure zero.

Published on 06 May 2026 - 2:43

score 146 · Answer 11 · 2026-04-13 03:41:43

146

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Markov Transition Kernels

Published on 13 Apr 2026 - 3:41

score 156 · Answer 12 · 2026-04-12 01:39:50

156

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$Var(f(X))$ when $Var(X)\to 0$

Published on 12 Apr 2026 - 1:39

score 723 · Answer 13 · 2026-04-14 19:19:53

723

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If $S$ is compact then the separating classes are same as convergence determining classes

Published on 14 Apr 2026 - 19:19

score 53 · Answer 14 · 2026-04-09 23:05:18

53

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Is there a term for "square-summable almost surely"?

Published on 09 Apr 2026 - 23:05

score 195 · Answer 15 · 2026-05-16 21:19:32

195

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Prove: If $E_1, E_2$ are measurable then $E_1\cup E_2$ are measurable

Published on 16 May 2026 - 21:19

List Question

Proving the Borel-Cantelli Lemma

Is the set of continuous functions measurable?

Is the set of Borel measurable transformations the closure of continuous functions under pointwise limits?

Comparing $\sigma$ algebras with topologies

Problem 4 part (a) from Stein's Real Analysis

Prove $h(y) = \int_{\mathbb{R}} f(x,y) dx$ is continuous if $f(x,y)$ is continuous for every fixed $x$ and $f(x,y)$ is integrable for every fixed $y$.

Is $\mu_X\otimes \mu_Y(A\times B)=\int_A \mu_Y(B^x)\mu_X(dx)$ hold if $X$ and $Y$ are not independents random variables?

The set at which a function's oscillation is at least $\epsilon$ is closed

Relationship between a parametric family of distributions and the measure of probability

$f$ is Riemann integrable if the set of discontinuities is measure zero.

Markov Transition Kernels

$Var(f(X))$ when $Var(X)\to 0$

If $S$ is compact then the separating classes are same as convergence determining classes

Is there a term for "square-summable almost surely"?

Prove: If $E_1, E_2$ are measurable then $E_1\cup E_2$ are measurable

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