Question

Borel $\sigma$-algebra of the order topology $\textit{vs.}$ $\sigma$-algebra generated by the topological subbasis

score 181 · Answer 1 · 2026-04-16 13:10:23

181

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Borel $\sigma$-algebra of the order topology $\textit{vs.}$ $\sigma$-algebra generated by the topological subbasis

Published on 16 Apr 2026 - 13:10

score 297 · Answer 2 · 2026-04-16 15:07:08

297

Views

Prove that $\lim_{n\rightarrow \infty} \int_{[-n,n]} f\,d\lambda= \int f\,d\lambda.$

Published on 16 Apr 2026 - 15:07

score 192 · Answer 3 · 2026-04-14 03:36:07

192

Views

Doob Dynkin lemma, uniqueness of the Borel function

Published on 14 Apr 2026 - 3:36

score 130 · Answer 4 · 2026-04-10 18:18:25

130

Views

Extension of measures by adding one extra set

Published on 10 Apr 2026 - 18:18

score 36 · Answer 5 · 2026-04-14 11:07:41

36

Views

Finding a sequence of sets whose limit is a given set

Published on 14 Apr 2026 - 11:07

score 35 · Answer 6 · 2026-04-14 16:52:58

35

Views

$\nu(A)=\int \mathcal{X}_{A}f(x)d\mu$ measure associated functional $l_{\nu}(g)=\int g(x)f(x)d\mu.$

Published on 14 Apr 2026 - 16:52

score 107 · Answer 7 · 2026-04-13 04:21:17

107

Views

What is a tube in $\mathbb{R}^n$?

Published on 13 Apr 2026 - 4:21

score 70 · Answer 8 · 2026-04-16 12:08:02

70

Views

The Hausdorff dimension (implication)

Published on 16 Apr 2026 - 12:08

score 233 · Answer 9 · 2026-04-13 08:39:34

233

Views

Measure on $C([0,1]^n)$

Published on 13 Apr 2026 - 8:39

score 347 · Answer 10 · 2026-04-08 15:28:47

347

Views

almost everywhere zero in product measure space

Published on 08 Apr 2026 - 15:28

score 362 · Answer 11 · 2026-04-14 06:49:44

362

Views

Lebesgue integration: integral of continuous function tends to infinity

Published on 14 Apr 2026 - 6:49

score 86 · Answer 12 · 2026-04-13 20:26:27

86

Views

Convergence of $\frac{\cos(x)}{n\sin(x)}$ an n$\rightarrow \infty$

Published on 13 Apr 2026 - 20:26

score 362 · Answer 13 · 2026-05-10 19:38:26

362

Views

Prove that if $E \subset \mathbb{R}^n $ has finite perimeter, then almost every vertical slice has finite perimeter too.

Published on 10 May 2026 - 19:38

score 117 · Answer 14 · 2026-04-11 23:36:03

117

Views

Holder continuity of Fourier transform of measure

Published on 11 Apr 2026 - 23:36

score 150 · Answer 15 · 2026-04-16 17:10:34

150

Views

Proof that $E(X|\sigma (G_1,G_2))=E(X|G_1)$, when $G_2,\sigma(\sigma(X),G_1)$ independent.

Published on 16 Apr 2026 - 17:10

List Question

Borel $\sigma$-algebra of the order topology $\textit{vs.}$ $\sigma$-algebra generated by the topological subbasis

Prove that $\lim_{n\rightarrow \infty} \int_{[-n,n]} f\,d\lambda= \int f\,d\lambda.$

Doob Dynkin lemma, uniqueness of the Borel function

Extension of measures by adding one extra set

Finding a sequence of sets whose limit is a given set

$\nu(A)=\int \mathcal{X}_{A}f(x)d\mu$ measure associated functional $l_{\nu}(g)=\int g(x)f(x)d\mu.$

What is a tube in $\mathbb{R}^n$?

The Hausdorff dimension (implication)

Measure on $C([0,1]^n)$

almost everywhere zero in product measure space

Lebesgue integration: integral of continuous function tends to infinity

Convergence of $\frac{\cos(x)}{n\sin(x)}$ an n$\rightarrow \infty$

Prove that if $E \subset \mathbb{R}^n $ has finite perimeter, then almost every vertical slice has finite perimeter too.

Holder continuity of Fourier transform of measure

Proof that $E(X|\sigma (G_1,G_2))=E(X|G_1)$, when $G_2,\sigma(\sigma(X),G_1)$ independent.

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