Question

Understanding Essential sup norm with simple functions

score 113 · Answer 1 · 2023-04-24 02:57:27

113

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Understanding Essential sup norm with simple functions

Published on 24 Apr 2023 - 2:57

score 56 · Answer 2 · 2023-04-24 17:19:59

56

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Suppose that you have uncountably many random variables satisfying $P(X_{\alpha} > x) < \eta$, then is $P(\sup X_{\alpha} > x) < \eta$ true?

Published on 24 Apr 2023 - 17:19

score 47 · Answer 3 · 2023-04-25 07:15:40

47

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Final part of the proof of $f$ is convex if and only if $f =\sup\{\varphi:\mathbb{R}^M\to \mathbb{R}: \varphi \le f, \varphi \text { affine} \}$

Published on 25 Apr 2023 - 7:15

score 147 · Answer 4 · 2023-04-27 04:48:15

147

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The greatest lower bound of $|\cos(x)+\sin(x)|$

Published on 27 Apr 2023 - 4:48

score 21 · Answer 5 · 2023-04-29 17:13:38

21

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Supremum of certain integrable functions

Published on 29 Apr 2023 - 17:13

score 62 · Answer 6 · 2023-05-02 03:45:36

62

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Prove or disprove infimum of B equals to supremum of A

Published on 02 May 2023 - 3:45

score 55 · Answer 7 · 2026-03-30 00:20:21

55

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Supremum of limit inferior

Published on 30 Mar 2026 - 0:20

score 123 · Answer 8 · 2023-05-08 10:11:10

123

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Find infimum and supremum of the function $f$ defined by the formula $f(x, y, z) = x^2 + y^2 + z^2$ on the set $A$

Published on 08 May 2023 - 10:11

score 74 · Answer 9 · 2023-05-08 16:11:02

74

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Uncountable ordered sets and monotonic functions: defining a sequence with a particular inferred restriction via induction

Published on 08 May 2023 - 16:11

score 97 · Answer 10 · 2023-05-09 08:22:45

97

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Prove that $\sup Z=\frac {\sup X}{\inf Y}$

Published on 09 May 2023 - 8:22

score 52 · Answer 11 · 2026-02-23 13:12:37

52

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(X,d) be a metric space. $F: X\to \overline{\mathbb{R}}$. $F$ is sequentially lower semicontinuous iff $F$ is lower semicontinuous

Published on 23 Feb 2026 - 13:12

score 99 · Answer 12 · 2026-03-29 21:56:59

99

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Sufficient condition that the Infimum of an uncountable family of measurable functions is measurable

Published on 29 Mar 2026 - 21:56

score 107 · Answer 13 · 2026-02-23 13:12:47

107

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$F$ is lower semicontinuous $\iff F(x)=\sup_{r>0}\inf_{y\in B(x,r)}F(y)$ for all $x\in X$

Published on 23 Feb 2026 - 13:12

score 56 · Answer 14 · 2023-05-13 15:06:40

56

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If $0<a<1$, then $\inf\{a^n:n\in\mathbb{Z}_+\}=0$.

Published on 13 May 2023 - 15:06

score 130 · Answer 15 · 2023-05-17 09:29:27

130

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Existence of supremum implies existence of infimum

Published on 17 May 2023 - 9:29

List Question

Understanding Essential sup norm with simple functions

Suppose that you have uncountably many random variables satisfying $P(X_{\alpha} > x) < \eta$, then is $P(\sup X_{\alpha} > x) < \eta$ true?

Final part of the proof of $f$ is convex if and only if $f =\sup\{\varphi:\mathbb{R}^M\to \mathbb{R}: \varphi \le f, \varphi \text { affine} \}$

The greatest lower bound of $|\cos(x)+\sin(x)|$

Supremum of certain integrable functions

Prove or disprove infimum of B equals to supremum of A

Supremum of limit inferior

Find infimum and supremum of the function $f$ defined by the formula $f(x, y, z) = x^2 + y^2 + z^2$ on the set $A$

Uncountable ordered sets and monotonic functions: defining a sequence with a particular inferred restriction via induction

Prove that $\sup Z=\frac {\sup X}{\inf Y}$

(X,d) be a metric space. $F: X\to \overline{\mathbb{R}}$. $F$ is sequentially lower semicontinuous iff $F$ is lower semicontinuous

Sufficient condition that the Infimum of an uncountable family of measurable functions is measurable

$F$ is lower semicontinuous $\iff F(x)=\sup_{r>0}\inf_{y\in B(x,r)}F(y)$ for all $x\in X$

If $0<a<1$, then $\inf\{a^n:n\in\mathbb{Z}_+\}=0$.

Existence of supremum implies existence of infimum

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