List questions from supremum-and-infimum

Published on 08 Jul 2020 - 22:48

240

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Prove that $\sup \{f(x)+g(x):\space x\in X\}\leq \sup \{f(x):\space x\in X\}+\sup \{g(x):\space x\in X\}$

Published on 09 Jul 2020 - 12:10

725

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Interchanging supremum with infimum

Published on 11 Jul 2020 - 18:17

764

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How to prove that supremum of strictly convex function is infinity?

Published on 12 Jul 2020 - 16:57

295

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Convexity conditions for an Infimum operation

Published on 23 Feb 2026 - 4:38

71

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How do we prove that $\sup_{n\geq 1}f_{n}$ is a measurable function when each term $f_{n}$ is measurable?

Published on 29 Mar 2026 - 11:44

479

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Find the lub and glb of a certain set

Published on 17 Jul 2020 - 1:02

458

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Equivalent definitions of essential supremum?

Published on 19 Jul 2020 - 16:19

57

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Is $\sup$ and $\inf$ of a set single?

Published on 20 Jul 2020 - 6:02

124

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To find supremum of this

Published on 21 Jul 2020 - 12:28

62

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Show that $\sup_{k \geq 1 }\inf_{n \geq k} a_n = \inf_{k \geq 1} \sup_{n \geq k} a_n$ for an alternating sequence

Published on 21 Jul 2020 - 19:03

66

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An equivalent condition of $f$ is integrable over $R\subseteq\mathbb{R}^2$

Published on 22 Jul 2020 - 2:09

66

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Continuity of infimum with respect to argument of predicate

Published on 22 Jul 2020 - 16:01

135

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there is a smallest positive number $p$ for which $f(p)=0$.

Published on 23 Jul 2020 - 18:51

47

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What is being "minimized" when discussing a confidence set?

Published on 28 Mar 2026 - 21:58

List Question

$A\subseteq\mathbb{R}$ is closed iff $\sup(A\cap[a,b])\in A$ and $\inf(A\cap[a,b])\in A$.

Prove that $\sup \{f(x)+g(x):\space x\in X\}\leq \sup \{f(x):\space x\in X\}+\sup \{g(x):\space x\in X\}$

Interchanging supremum with infimum

How to prove that supremum of strictly convex function is infinity?

Convexity conditions for an Infimum operation

How do we prove that $\sup_{n\geq 1}f_{n}$ is a measurable function when each term $f_{n}$ is measurable?

Find the lub and glb of a certain set

Equivalent definitions of essential supremum?

Is $\sup$ and $\inf$ of a set single?

To find supremum of this

Show that $\sup_{k \geq 1 }\inf_{n \geq k} a_n = \inf_{k \geq 1} \sup_{n \geq k} a_n$ for an alternating sequence

An equivalent condition of $f$ is integrable over $R\subseteq\mathbb{R}^2$

Continuity of infimum with respect to argument of predicate

there is a smallest positive number $p$ for which $f(p)=0$.

What is being "minimized" when discussing a confidence set?

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