Question

Why is Wiener measure a Gaussian measure?

score 490 · Answer 1 · 2026-04-14 07:03:41

Why is Wiener measure a Gaussian measure?

Published on 14 Apr 2026 - 7:03

score 59 · Answer 2 · 2026-04-14 18:58:22

Can any sense be made of the following conjecture? For any given $x$ in $[0,1]$, "most" measure 1 subsets of $ [0,1]$ contain $ x$.

score 135 · Answer 3 · 2026-04-12 02:03:17

135

Views

Young measure generated by sequence

Published on 12 Apr 2026 - 2:03

score 84 · Answer 4 · 2026-04-15 07:38:13

84

Views

Solve $\int_{[0,\infty[}(\int_{[0,\infty[} e^{-xy}\sin{x} \sin{y} d\lambda(x)) d\lambda(y)$

Published on 15 Apr 2026 - 7:38

score 100 · Answer 5 · 2026-04-16 01:33:44

100

Views

compute $\lim_{n \to \infty} \int_{[0,1]} \frac{(\ln x)^n}{\sqrt{1-x^2}} \, dx$

Published on 16 Apr 2026 - 1:33

score 397 · Answer 6 · 2026-04-16 15:16:26

397

Views

Proving that every Cauchy sequence in measure converges in measure

Published on 16 Apr 2026 - 15:16

score 172 · Answer 7 · 2026-04-16 12:08:27

172

Views

Are all conditions met for Fubini? Needed to work out $\lim_{R\to \infty}\int_{[0,R]}\frac{\sin{x}}{x}d \lambda (x)$

Published on 16 Apr 2026 - 12:08

score 677 · Answer 8 · 2026-04-14 03:59:11

677

Views

Is the sigma algebra generated by $X$ random variable and its square equal to the sigma algebra generated by $X$ alone?

Published on 14 Apr 2026 - 3:59

score 81 · Answer 9 · 2026-04-16 00:42:54

81

Views

Use of Tonelli's Theorem to calculate $\int_{[0,\infty[} (\int_{[0,\infty[}xe^{-x^{2}(1+y^{2})}d\lambda (x)) d\lambda (y)$

Published on 16 Apr 2026 - 0:42

score 106 · Answer 10 · 2026-04-03 18:37:56

106

Views

$\mathbb{E}X^2 = \mathbb{E}Y^2$ and $\mathbb{E}(Y|\mathcal{A}) = X$ P-a.s. $\Rightarrow X=Y$ P.-a.s.

Published on 03 Apr 2026 - 18:37

score 449 · Answer 11 · 2026-04-13 02:36:07

449

Views

Functional Analysis Reference Books

Published on 13 Apr 2026 - 2:36

score 93 · Answer 12 · 2026-05-05 23:21:49

93

Views

Can I define a measurable function using base of a topology?

Published on 05 May 2026 - 23:21

score 384 · Answer 13 · 2026-05-01 08:29:03

384

Views

Proof that $\sigma$-algebra is not countable (proof revision)

Published on 01 May 2026 - 8:29

score 171 · Answer 14 · 2026-04-15 04:16:34

171

Views

Show that T is continuos linear functional and find the norm of T

Published on 15 Apr 2026 - 4:16

score 65 · Answer 15 · 2026-04-13 23:59:59

65

Views

Double Integral unequal after switching $dy$ and $dx$. Exact reasoning required

Published on 13 Apr 2026 - 23:59

List Question

Why is Wiener measure a Gaussian measure?

Can any sense be made of the following conjecture? For any given $x$ in $[0,1]$, "most" measure 1 subsets of $ [0,1]$ contain $ x$.

Young measure generated by sequence

Solve $\int_{[0,\infty[}(\int_{[0,\infty[} e^{-xy}\sin{x} \sin{y} d\lambda(x)) d\lambda(y)$

compute $\lim_{n \to \infty} \int_{[0,1]} \frac{(\ln x)^n}{\sqrt{1-x^2}} \, dx$

Proving that every Cauchy sequence in measure converges in measure

Are all conditions met for Fubini? Needed to work out $\lim_{R\to \infty}\int_{[0,R]}\frac{\sin{x}}{x}d \lambda (x)$

Is the sigma algebra generated by $X$ random variable and its square equal to the sigma algebra generated by $X$ alone?

Use of Tonelli's Theorem to calculate $\int_{[0,\infty[} (\int_{[0,\infty[}xe^{-x^{2}(1+y^{2})}d\lambda (x)) d\lambda (y)$

$\mathbb{E}X^2 = \mathbb{E}Y^2$ and $\mathbb{E}(Y|\mathcal{A}) = X$ P-a.s. $\Rightarrow X=Y$ P.-a.s.

Functional Analysis Reference Books

Can I define a measurable function using base of a topology?

Proof that $\sigma$-algebra is not countable (proof revision)

Show that T is continuos linear functional and find the norm of T

Double Integral unequal after switching $dy$ and $dx$. Exact reasoning required

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