Question

$\mathrm{ess\, sup}(f)=\text{sup}(f)$ for a continuous non negative function $f$

score 705 · Answer 1 · 2026-04-14 07:18:08

705

Views

$\mathrm{ess\, sup}(f)=\text{sup}(f)$ for a continuous non negative function $f$

Published on 14 Apr 2026 - 7:18

score 267 · Answer 2 · 2026-04-30 03:42:08

267

Views

If $\{X_\alpha\}$ is a collection of mutually disjoint meas. subsets of $\mathbb{R} \rightarrow$ then at most countable of them has positive measure.

Published on 30 Apr 2026 - 3:42

score 58 · Answer 3 · 2026-04-30 03:42:09

58

Views

A question about the number of possible $\sigma$-algebras

Published on 30 Apr 2026 - 3:42

score 706 · Answer 4 · 2026-04-12 18:53:12

706

Views

Prove that $X : \Omega \to \Bbb R$ is a random variable if $X$ is constant.

Published on 12 Apr 2026 - 18:53

score 103 · Answer 5 · 2026-04-30 08:07:16

103

Views

If $f\in L^1(\mu)$ then $f$ is finite $\mu$-a.e.

Published on 30 Apr 2026 - 8:07

score 211 · Answer 6 · 2026-04-11 08:35:56

211

Views

Reverse kernel of a Markov kernel with density

Published on 11 Apr 2026 - 8:35

score 51 · Answer 7 · 2026-04-13 02:41:45

51

Views

Does this function define a probability function?

Published on 13 Apr 2026 - 2:41

score 68 · Answer 8 · 2026-05-10 17:38:10

68

Views

Doubt in variant of Holder inequality

Published on 10 May 2026 - 17:38

score 89 · Answer 9 · 2026-04-16 17:53:01

89

Views

$\int_0^\infty\frac{x\log(x)}{(1+x)^3}dx$ converges in making use of the sequence

Published on 16 Apr 2026 - 17:53

score 100 · Answer 10 · 2026-05-11 01:53:19

100

Views

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

Published on 11 May 2026 - 1:53

score 2.2k · Answer 11 · 2026-04-15 03:04:36

2.2k

Views

What is the canonical process of a measure space $(\Omega, \mathscr{F}, \mathbb{Q})$?

Published on 15 Apr 2026 - 3:04

score 106 · Answer 12 · 2026-05-11 18:45:50

106

Views

A proposition about bounded and weak-$L^2$ integrable fucntion

Published on 11 May 2026 - 18:45

score 66 · Answer 13 · 2026-04-14 11:28:36

66

Views

Measure theory: density of $\mathbb{Q}$ in $\mathbb{R}$ exercise

Published on 14 Apr 2026 - 11:28

score 296 · Answer 14 · 2026-04-13 02:59:55

296

Views

A basic exercise about Lebesgue's Dominated Convergence Theorem

Published on 13 Apr 2026 - 2:59

score 176 · Answer 15 · 2026-04-11 01:17:40

176

Views

Example of a subset of $\mathbb{R}^2$ which is not $\sigma$-finite under Lebesgue measure?

Published on 11 Apr 2026 - 1:17

List Question

$\mathrm{ess\, sup}(f)=\text{sup}(f)$ for a continuous non negative function $f$

If $\{X_\alpha\}$ is a collection of mutually disjoint meas. subsets of $\mathbb{R} \rightarrow$ then at most countable of them has positive measure.

A question about the number of possible $\sigma$-algebras

Prove that $X : \Omega \to \Bbb R$ is a random variable if $X$ is constant.

If $f\in L^1(\mu)$ then $f$ is finite $\mu$-a.e.

Reverse kernel of a Markov kernel with density

Does this function define a probability function?

Doubt in variant of Holder inequality

$\int_0^\infty\frac{x\log(x)}{(1+x)^3}dx$ converges in making use of the sequence

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

What is the canonical process of a measure space $(\Omega, \mathscr{F}, \mathbb{Q})$?

A proposition about bounded and weak-$L^2$ integrable fucntion

Measure theory: density of $\mathbb{Q}$ in $\mathbb{R}$ exercise

A basic exercise about Lebesgue's Dominated Convergence Theorem

Example of a subset of $\mathbb{R}^2$ which is not $\sigma$-finite under Lebesgue measure?

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