List questions from supremum-and-infimum

Published on 24 Jul 2020 - 15:57

679

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Let $A$ be a subset of $\mathbb{R}$ such that $A$ is bounded below with inf $A = L > 0$.

Published on 25 Jul 2020 - 13:43

150

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What is the supremum, infimum, maximum and minimum of the set $B:=\{x \in\mathbb{R}, \left||x-1|-|x-2|\right|<1\}$?

Published on 26 Jul 2020 - 7:56

165

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Interchange max and sup in a function space

Published on 30 Mar 2026 - 20:36

412

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How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Published on 28 Jul 2020 - 6:48

177

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Abuse of notation for infimum and supremum

Published on 25 Mar 2026 - 17:32

50

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$\sup_{x \in \mathbb R} k^2e^{−kx^2}f(x)≤\sup_{x \in \mathbb R} (k+1)^2e^{−(k+1)x^2}f(x)$?

Published on 09 Jul 2016 - 20:35

470

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Proving the supremum of this set

Published on 10 Jul 2016 - 11:47

2.3k

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How to find the supremum and infimum of this set?

Published on 11 Jul 2016 - 20:31

194

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Doob's submartingale theorem

Published on 15 Jul 2016 - 18:14

299

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Exchanging supremum and conditional expectation

Published on 30 Mar 2026 - 15:31

6.2k

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Is there a meaning to the notation "\arg \sup"?

Published on 18 Jul 2016 - 6:37

2.8k

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Prove that $\sup{A} = \inf{B}$ if and only if for each $\delta > 0$ there exists $x \in A$ and $y \in B$ such that $x + \delta > y$:

Published on 20 Jul 2016 - 5:48

306

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Relation between Supremum and limit superior

Published on 28 Mar 2026 - 21:50

381

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If $A$ is infinite and bounded, the infimum of the difference set of $A$ is zero.

Published on 23 Jul 2016 - 6:27

List Question

How can I prove that $\sup(A) = \sup(B)$

Let $A$ be a subset of $\mathbb{R}$ such that $A$ is bounded below with inf $A = L > 0$.

What is the supremum, infimum, maximum and minimum of the set $B:=\{x \in\mathbb{R}, \left||x-1|-|x-2|\right|<1\}$?

Interchange max and sup in a function space

How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Abuse of notation for infimum and supremum

$\sup_{x \in \mathbb R} k^2e^{−kx^2}f(x)≤\sup_{x \in \mathbb R} (k+1)^2e^{−(k+1)x^2}f(x)$?

Proving the supremum of this set

How to find the supremum and infimum of this set?

Doob's submartingale theorem

Exchanging supremum and conditional expectation

Is there a meaning to the notation "\arg \sup"?

Prove that $\sup{A} = \inf{B}$ if and only if for each $\delta > 0$ there exists $x \in A$ and $y \in B$ such that $x + \delta > y$:

Relation between Supremum and limit superior

If $A$ is infinite and bounded, the infimum of the difference set of $A$ is zero.

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