Question

Existence of sequence converging to the supremum over all measuable sets in $(\Omega, \mathcal{F})$.

score 99 · Answer 1 · 2022-10-08 22:11:03

99

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Existence of sequence converging to the supremum over all measuable sets in $(\Omega, \mathcal{F})$.

Published on 08 Oct 2022 - 22:11

score 53 · Answer 2 · 2022-10-09 14:51:59

53

Views

is $\lim_{n\to \infty} \sup_{i \in I}(x^n_i) =\sup_{i \in I}(\lim_{n\to\infty}(x^n_i)$? for each i, $x_i^n$ is a monotone increasing sequence.

Published on 09 Oct 2022 - 14:51

score 184 · Answer 3 · 2022-10-11 01:53:36

184

Views

Please check my proof that $\inf(bS) = b\sup(S)$ when $b<0$

Published on 11 Oct 2022 - 1:53

score 117 · Answer 4 · 2022-10-11 14:45:19

117

Views

Set of lower bounds not containing a greatest member

Published on 11 Oct 2022 - 14:45

score 44 · Answer 5 · 2026-03-25 09:31:49

44

Views

Question on definition for proving a theorem regarding simulation.

Published on 25 Mar 2026 - 9:31

score 41 · Answer 6 · 2022-10-14 00:59:47

41

Views

For nonemptyset $A\subset \mathbb R$, there exists $\{a_n\}\subset A$ s.t. $\lim a_n=\inf A.$

Published on 14 Oct 2022 - 0:59

score 45 · Answer 7 · 2022-10-14 02:13:28

45

Views

Prove there eixsts $u\in A, v\in B$ s.t. $\inf\{\|a-b\| \mid a\in A, b\in B\}=\|u-v\|$, for compact $A$ and closed $B$.

Published on 14 Oct 2022 - 2:13

score 41 · Answer 8 · 2026-04-08 22:12:17

41

Views

How to calculate $\inf_Y\sup_Xf(x,y)$ correctly?

Published on 08 Apr 2026 - 22:12

score 202 · Answer 9 · 2026-04-11 13:00:13

202

Views

Bounds of sin(x) where x is rational

Published on 11 Apr 2026 - 13:00

score 115 · Answer 10 · 2022-10-15 15:20:23

115

Views

I want to prove $f$ in continuous on $[a,b]$ implies $F(x)=\sup f([a,x])$ is continuous on $[a,b]$?

Published on 15 Oct 2022 - 15:20

score 90 · Answer 11 · 2022-10-20 19:24:58

90

Views

Proof that $a_{n}:=\sup\{|\frac{nx}{1+n^2x^2}|:x\in \mathbb{R}|\}$ $(n\in \mathbb{N})$ does not converge to $0$

Published on 20 Oct 2022 - 19:24

score 43 · Answer 12 · 2022-10-21 15:34:06

43

Views

Is $\text{ess sup}_{x\in X}\text{ess sup}_{y\in Y} f(x,y)=\text{ess sup}_{y\in Y}\text{ess sup}_{x\in X} f(x,y)$ true?

Published on 21 Oct 2022 - 15:34

score 33 · Answer 13 · 2026-04-03 00:55:47

33

Views

When is the supremum of a vector field finite?

Published on 03 Apr 2026 - 0:55

score 110 · Answer 14 · 2026-04-10 00:15:33

110

Views

Can I interchange $\max$ and $\sup$?

Published on 10 Apr 2026 - 0:15

score 129 · Answer 15 · 2022-10-30 19:25:21

129

Views

How to prove a totally ordered set is not Dedekind complete?

Published on 30 Oct 2022 - 19:25

List Question

Existence of sequence converging to the supremum over all measuable sets in $(\Omega, \mathcal{F})$.

is $\lim_{n\to \infty} \sup_{i \in I}(x^n_i) =\sup_{i \in I}(\lim_{n\to\infty}(x^n_i)$? for each i, $x_i^n$ is a monotone increasing sequence.

Please check my proof that $\inf(bS) = b\sup(S)$ when $b<0$

Set of lower bounds not containing a greatest member

Question on definition for proving a theorem regarding simulation.

For nonemptyset $A\subset \mathbb R$, there exists $\{a_n\}\subset A$ s.t. $\lim a_n=\inf A.$

Prove there eixsts $u\in A, v\in B$ s.t. $\inf\{\|a-b\| \mid a\in A, b\in B\}=\|u-v\|$, for compact $A$ and closed $B$.

How to calculate $\inf_Y\sup_Xf(x,y)$ correctly?

Bounds of sin(x) where x is rational

I want to prove $f$ in continuous on $[a,b]$ implies $F(x)=\sup f([a,x])$ is continuous on $[a,b]$?

Proof that $a_{n}:=\sup\{|\frac{nx}{1+n^2x^2}|:x\in \mathbb{R}|\}$ $(n\in \mathbb{N})$ does not converge to $0$

Is $\text{ess sup}_{x\in X}\text{ess sup}_{y\in Y} f(x,y)=\text{ess sup}_{y\in Y}\text{ess sup}_{x\in X} f(x,y)$ true?

When is the supremum of a vector field finite?

Can I interchange $\max$ and $\sup$?

How to prove a totally ordered set is not Dedekind complete?

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