Question

Is $\text{ess sup}_{P\in \mathscr P}E_P[X]=\sup_{P \in \mathscr P}E_P[X]$ for nonnegative $X$?

score 52 · Answer 1 · 2022-11-21 19:24:16

52

Views

Is $\text{ess sup}_{P\in \mathscr P}E_P[X]=\sup_{P \in \mathscr P}E_P[X]$ for nonnegative $X$?

Published on 21 Nov 2022 - 19:24

score 126 · Answer 2 · 2022-11-22 11:36:05

126

Views

Let $f:A \times B \to \mathbb R \cup \{\pm\infty\}$. Then $\sup_{a \in A} \sup_{b \in B} f(a,b) = \sup_{(a,b) \in A \times B} f(a,b)$

Published on 22 Nov 2022 - 11:36

score 212 · Answer 3 · 2026-04-11 15:56:47

212

Views

How can I prove that sup(A)=infinity in this situation?

Published on 11 Apr 2026 - 15:56

score 84 · Answer 4 · 2022-11-22 18:24:58

84

Views

Why is $\sup_k \inf_t E[X_t^{(k)}] \le \inf_t \sup_k E[X_t^{(k)}]$ obvious?

Published on 22 Nov 2022 - 18:24

score 21 · Answer 5 · 2022-11-22 21:00:43

21

Views

If $F$ is convex, then so is $x \mapsto \inf_{y\in Y} F(x, y)$

Published on 22 Nov 2022 - 21:00

score 96 · Answer 6 · 2022-11-23 18:15:58

96

Views

Consider the set $\;A = \left\{\frac5{x−3}:x>3\right\}$. How do I prove that $0$ is the infimum?

Published on 23 Nov 2022 - 18:15

score 25 · Answer 7 · 2026-04-10 18:06:04

25

Views

Does the following sequence of min-max converge?

Published on 10 Apr 2026 - 18:06

score 27 · Answer 8 · 2022-11-27 14:00:56

27

Views

How can I prove the equality of $\sup(A)$ and $sup(A\setminus B)?$

Published on 27 Nov 2022 - 14:00

score 63 · Answer 9 · 2026-04-11 16:51:58

63

Views

0.Finding 2 sets A and B(belong to R) that SupA = SupB, infA=infB and a=!b for all a and all b

Published on 11 Apr 2026 - 16:51

score 31 · Answer 10 · 2022-12-02 01:42:11

Is it implied that sup and inf are just real numbers? When discussing a subset of $\mathbb Q$, does the sup have to be in $\mathbb Q$ to exist?

score 67 · Answer 11 · 2026-04-10 09:08:14

67

Views

Doubt about two different ways of taking the supremum of a sequence of functions

Published on 10 Apr 2026 - 9:08

score 39 · Answer 12 · 2022-12-04 09:22:25

39

Views

Proving that for $f\in C^2(a,\infty)$ then $\max_{(a,\infty)} |f'(x) |\le 4\max_{(a,\infty)}|f(x)|\max_{(a,\infty)} |f''(x) |$.

Published on 04 Dec 2022 - 9:22

score 52 · Answer 13 · 2026-04-07 19:03:46

52

Views

Trouble with proving that if $(a_n)_n,(b_n)_n$ and $a_n \le b_n \forall n \ge \nu$ then $\liminf_n a_n \le \liminf_n b_n$

Published on 07 Apr 2026 - 19:03

score 435 · Answer 14 · 2026-04-09 00:19:05

435

Views

Regular polygon with diagonals: bounds on area of largest cell?

Published on 09 Apr 2026 - 0:19

score 69 · Answer 15 · 2022-12-09 08:29:10

69

Views

Finding $\sup$,$\inf$,$\max$ $\min$ of set $A=\{x \in \Bbb R | x=\frac{(-1)^{n+1}}{n+1} + \frac{1+(-1)^n}{2}\}$

Published on 09 Dec 2022 - 8:29

List Question

Is $\text{ess sup}_{P\in \mathscr P}E_P[X]=\sup_{P \in \mathscr P}E_P[X]$ for nonnegative $X$?

Let $f:A \times B \to \mathbb R \cup \{\pm\infty\}$. Then $\sup_{a \in A} \sup_{b \in B} f(a,b) = \sup_{(a,b) \in A \times B} f(a,b)$

How can I prove that sup(A)=infinity in this situation?

Why is $\sup_k \inf_t E[X_t^{(k)}] \le \inf_t \sup_k E[X_t^{(k)}]$ obvious?

If $F$ is convex, then so is $x \mapsto \inf_{y\in Y} F(x, y)$

Consider the set $\;A = \left\{\frac5{x−3}:x>3\right\}$. How do I prove that $0$ is the infimum?

Does the following sequence of min-max converge?

How can I prove the equality of $\sup(A)$ and $sup(A\setminus B)?$

0.Finding 2 sets A and B(belong to R) that SupA = SupB, infA=infB and a=!b for all a and all b

Is it implied that sup and inf are just real numbers? When discussing a subset of $\mathbb Q$, does the sup have to be in $\mathbb Q$ to exist?

Doubt about two different ways of taking the supremum of a sequence of functions

Proving that for $f\in C^2(a,\infty)$ then $\max_{(a,\infty)} |f'(x) |\le 4\max_{(a,\infty)}|f(x)|\max_{(a,\infty)} |f''(x) |$.

Trouble with proving that if $(a_n)_n,(b_n)_n$ and $a_n \le b_n \forall n \ge \nu$ then $\liminf_n a_n \le \liminf_n b_n$

Regular polygon with diagonals: bounds on area of largest cell?

Finding $\sup$,$\inf$,$\max$ $\min$ of set $A=\{x \in \Bbb R | x=\frac{(-1)^{n+1}}{n+1} + \frac{1+(-1)^n}{2}\}$

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