Question

If $R$ is a $\sigma - $ring then {$E\in X|E\in R$ or $E^c \in R$ } is a $\sigma$ -algebra

score 898 · Answer 1 · 2026-04-14 14:27:03

898

Views

If $R$ is a $\sigma - $ring then {$E\in X|E\in R$ or $E^c \in R$ } is a $\sigma$ -algebra

Published on 14 Apr 2026 - 14:27

score 120 · Answer 2 · 2026-04-14 18:30:33

120

Views

Does absolute continuity preserve tightness of probability measures on separable metric spaces?

Published on 14 Apr 2026 - 18:30

score 89 · Answer 3 · 2026-05-10 16:56:44

89

Views

Asymptotics of integrals with respect to asymptotically equivalent distribution functions

Published on 10 May 2026 - 16:56

score 49 · Answer 4 · 2026-04-12 11:24:32

49

Views

$d(\xi, \eta) = H_{\mu}(\xi|\eta) + H_{\mu}(\eta|\xi)$ defines a metric

Published on 12 Apr 2026 - 11:24

score 331 · Answer 5 · 2026-05-10 22:09:27

331

Views

Show that $f$ is $\mathbf{X}$-measurable iff $f^{-1}(E)\in\mathbf{X}$ for every Borel set $E$.

Published on 10 May 2026 - 22:09

score 543 · Answer 6 · 2026-04-11 02:17:05

543

Views

Convergence in Egorov's theorem

Published on 11 Apr 2026 - 2:17

score 61 · Answer 7 · 2026-04-09 03:15:05

61

Views

Storing numbers in an efficient way in computer.

Published on 09 Apr 2026 - 3:15

score 112 · Answer 8 · 2026-03-25 12:47:29

112

Views

independence implies integrability?!

Published on 25 Mar 2026 - 12:47

score 61 · Answer 9 · 2026-04-10 16:45:01

61

Views

Two dimensional Laplace transform of convolutions

Published on 10 Apr 2026 - 16:45

score 44 · Answer 10 · 2026-04-16 07:59:37

44

Views

$-\liminf _n |f-f_n|d\mu=\limsup_n |f-f_n|d\mu$, is this actually a true claim?

Published on 16 Apr 2026 - 7:59

score 100 · Answer 11 · 2026-04-10 17:47:01

100

Views

Integration measures, subtraction and absolute value

Published on 10 Apr 2026 - 17:47

score 48 · Answer 12 · 2026-04-15 12:35:44

Define the function $F\mathop: \mathbb{R} \to [0,\infty)$ by $\displaystyle{F(x):= \mu \left((-\infty,x] \right)}$. Prove the following.

score 99 · Answer 13 · 2026-03-25 12:44:51

99

Views

Can the rank of the differential of a Lipschitz map decrease in a small neighbourhood?

Published on 25 Mar 2026 - 12:44

score 146 · Answer 14 · 2026-05-15 08:15:34

146

Views

Convolution of molifiers with measure

Published on 15 May 2026 - 8:15

score 48 · Answer 15 · 2026-04-16 07:23:20

48

Views

Problem with showing the integrability of $\int_{B}(x^2+y^2)^{-3/2}d\lambda^2(x,y)$

Published on 16 Apr 2026 - 7:23

List Question

If $R$ is a $\sigma - $ring then {$E\in X|E\in R$ or $E^c \in R$ } is a $\sigma$ -algebra

Does absolute continuity preserve tightness of probability measures on separable metric spaces?

Asymptotics of integrals with respect to asymptotically equivalent distribution functions

$d(\xi, \eta) = H_{\mu}(\xi|\eta) + H_{\mu}(\eta|\xi)$ defines a metric

Show that $f$ is $\mathbf{X}$-measurable iff $f^{-1}(E)\in\mathbf{X}$ for every Borel set $E$.

Convergence in Egorov's theorem

Storing numbers in an efficient way in computer.

independence implies integrability?!

Two dimensional Laplace transform of convolutions

$-\liminf _n |f-f_n|d\mu=\limsup_n |f-f_n|d\mu$, is this actually a true claim?

Integration measures, subtraction and absolute value

Define the function $F\mathop: \mathbb{R} \to [0,\infty)$ by $\displaystyle{F(x):= \mu \left((-\infty,x] \right)}$. Prove the following.

Can the rank of the differential of a Lipschitz map decrease in a small neighbourhood?

Convolution of molifiers with measure

Problem with showing the integrability of $\int_{B}(x^2+y^2)^{-3/2}d\lambda^2(x,y)$

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