Question

Finding an example satisfying $\mu(A)=3/4$, $\mu(B)=2/3$ and $\mu(A\cap B)$

score 47 · Answer 1 · 2026-04-15 02:35:52

47

Views

Finding an example satisfying $\mu(A)=3/4$, $\mu(B)=2/3$ and $\mu(A\cap B)$

Published on 15 Apr 2026 - 2:35

score 401 · Answer 2 · 2026-04-10 11:00:13

401

Views

Proof of a criterion for Bochner integrability

Published on 10 Apr 2026 - 11:00

score 132 · Answer 3 · 2026-04-11 00:07:23

132

Views

Does Cauchy imply boundedness?

Published on 11 Apr 2026 - 0:07

score 519 · Answer 4 · 2026-04-12 04:29:52

519

Views

Uniqueness of Lebesgue measure on $S^n$

Published on 12 Apr 2026 - 4:29

score 33 · Answer 5 · 2026-04-13 19:22:28

33

Views

Clarification regarding existence in case of Monotone Convergence Theorem

Published on 13 Apr 2026 - 19:22

score 522 · Answer 6 · 2026-04-14 21:30:23

Show the outer measure of $A \subseteq \mathbf{R}$ is equal to the limit as $n\rightarrow \infty$ of $A\cap[-n,n]$

score 54 · Answer 7 · 2026-04-14 23:43:45

54

Views

How can $\bigcup\limits_{i=1}^{\infty}E_i\in\mathscr{R}$?

Published on 14 Apr 2026 - 23:43

score 411 · Answer 8 · 2026-04-09 01:32:14

411

Views

What Jensen inequality implies in it holds with equality

Published on 09 Apr 2026 - 1:32

score 4.6k · Answer 9 · 2026-04-12 16:46:24

4.6k

Views

Approximation of measurable function via simple functions [Proof]

Published on 12 Apr 2026 - 16:46

score 53 · Answer 10 · 2026-04-09 17:15:34

53

Views

$\mu(\bigcup_{n=N}^\infty\omega:|g_n(\omega)-g(\omega)|>\varepsilon)<\varepsilon$ then $g_n\to g$ pointwise a.e.

Published on 09 Apr 2026 - 17:15

score 71 · Answer 11 · 2026-04-12 07:01:59

71

Views

Is the $\pi$-system generated by a topology the topology itself?

Published on 12 Apr 2026 - 7:01

score 940 · Answer 12 · 2026-04-11 07:34:11

940

Views

Joint convergence in distribution of independent random variables

Published on 11 Apr 2026 - 7:34

score 60 · Answer 13 · 2026-04-16 19:37:03

$\int\sum|f_n-f| \, d\mu< \infty \implies \mu( \bigcup\{\omega: |f_n(\omega) - f(\omega)| > \varepsilon\}) < \varepsilon$

score 359 · Answer 14 · 2026-04-10 08:19:19

359

Views

What is a bijection between CDF and characteristic function?

Published on 10 Apr 2026 - 8:19

score 350 · Answer 15 · 2026-04-13 01:22:28

350

Views

What is the Borel $\sigma$-algebra of $\mathbb R^{[0,\infty)}$?

Published on 13 Apr 2026 - 1:22

List Question

Finding an example satisfying $\mu(A)=3/4$, $\mu(B)=2/3$ and $\mu(A\cap B)$

Proof of a criterion for Bochner integrability

Does Cauchy imply boundedness?

Uniqueness of Lebesgue measure on $S^n$

Clarification regarding existence in case of Monotone Convergence Theorem

Show the outer measure of $A \subseteq \mathbf{R}$ is equal to the limit as $n\rightarrow \infty$ of $A\cap[-n,n]$

How can $\bigcup\limits_{i=1}^{\infty}E_i\in\mathscr{R}$?

What Jensen inequality implies in it holds with equality

Approximation of measurable function via simple functions [Proof]

$\mu(\bigcup_{n=N}^\infty\omega:|g_n(\omega)-g(\omega)|>\varepsilon)<\varepsilon$ then $g_n\to g$ pointwise a.e.

Is the $\pi$-system generated by a topology the topology itself?

Joint convergence in distribution of independent random variables

$\int\sum|f_n-f| \, d\mu< \infty \implies \mu( \bigcup\{\omega: |f_n(\omega) - f(\omega)| > \varepsilon\}) < \varepsilon$

What is a bijection between CDF and characteristic function?

What is the Borel $\sigma$-algebra of $\mathbb R^{[0,\infty)}$?

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