Question

Showing that the supremum of a given function is finite.

score 90 · Answer 1 · 2024-03-02 21:27:14

90

Views

Showing that the supremum of a given function is finite.

Published on 02 Mar 2024 - 21:27

score 77 · Answer 2 · 2026-02-23 14:47:19

77

Views

Property of lower semicontinuous functions

Published on 23 Feb 2026 - 14:47

score 48 · Answer 3 · 2024-03-13 18:11:54

48

Views

$\sup$ and $\inf$ of $\{a - \frac1n|n\in \mathbb N^*\}$

Published on 13 Mar 2024 - 18:11

score 39 · Answer 4 · 2026-03-29 02:45:22

39

Views

A supremum on orthogonal matrices

Published on 29 Mar 2026 - 2:45

score 33 · Answer 5 · 2024-03-17 04:36:40

33

Views

Assuming that $(f_n)_n$ is bounded, does $\sup_{n\in\mathbb N}||f_n||_H <+\infty$ hold?

Published on 17 Mar 2024 - 4:36

score 17 · Answer 6 · 2026-03-13 06:04:17

17

Views

An inequality involving infimums of the scaled $k$-th moment and of a scaled moment-generating function.

Published on 13 Mar 2026 - 6:04

score 61 · Answer 7 · 2024-03-25 15:09:27

61

Views

How to prove that ${\displaystyle \, \, \lim_{r \to 0} \, \sup_{x \in \mathbb R^n} \, r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy = 0}$?

Published on 25 Mar 2024 - 15:09

score 100 · Answer 8 · 2024-03-26 20:09:30

100

Views

How to prove that $ {\displaystyle \sup_{x \in \mathbb R^n, \, r > 0} r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy < \infty}$?

Published on 26 Mar 2024 - 20:09

score 35 · Answer 9 · 2024-03-26 21:17:28

35

Views

Determine the infimum of a function

Published on 26 Mar 2024 - 21:17

score 53 · Answer 10 · 2024-03-29 15:08:56

53

Views

$\sup_x(y \cdot f(x)+b(x)-1/2\lVert f(x) \rVert^2)$ convex and regular with respect to $y$?

Published on 29 Mar 2024 - 15:08

score 16 · Answer 11 · 2026-03-08 10:20:56

16

Views

Prove that if a curve y(x) is concave, (dy/dx, y-intercept of tangent to curve with slope dy/dx) are the coordinates of g(t), the supremum of y-tx

Published on 08 Mar 2026 - 10:20

score 708 · Answer 12 · 2015-01-03 18:55:32

708

Views

Show that sets of real numbers $A, B$ are adjacent iff $\sup A = \inf B$

Published on 03 Jan 2015 - 18:55

score 2.5k · Answer 13 · 2015-01-06 16:56:38

2.5k

Views

Find the infimum (with proof) of the set $ X = \left \{ x \in \mathbb{R} : x^{2} < 3 \right \} $

Published on 06 Jan 2015 - 16:56

score 583 · Answer 14 · 2015-01-07 23:25:11

583

Views

Proof on infimum and supremum

Published on 07 Jan 2015 - 23:25

score 1.2k · Answer 15 · 2015-01-08 21:02:56

1.2k

Views

Proof of theorem in infimum and supremum

Published on 08 Jan 2015 - 21:02

List Question

Showing that the supremum of a given function is finite.

Property of lower semicontinuous functions

$\sup$ and $\inf$ of $\{a - \frac1n|n\in \mathbb N^*\}$

A supremum on orthogonal matrices

Assuming that $(f_n)_n$ is bounded, does $\sup_{n\in\mathbb N}||f_n||_H <+\infty$ hold?

An inequality involving infimums of the scaled $k$-th moment and of a scaled moment-generating function.

How to prove that ${\displaystyle \, \, \lim_{r \to 0} \, \sup_{x \in \mathbb R^n} \, r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy = 0}$?

How to prove that $ {\displaystyle \sup_{x \in \mathbb R^n, \, r > 0} r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy < \infty}$?

Determine the infimum of a function

$\sup_x(y \cdot f(x)+b(x)-1/2\lVert f(x) \rVert^2)$ convex and regular with respect to $y$?

Prove that if a curve y(x) is concave, (dy/dx, y-intercept of tangent to curve with slope dy/dx) are the coordinates of g(t), the supremum of y-tx

Show that sets of real numbers $A, B$ are adjacent iff $\sup A = \inf B$

Find the infimum (with proof) of the set $ X = \left \{ x \in \mathbb{R} : x^{2} < 3 \right \} $

Proof on infimum and supremum

Proof of theorem in infimum and supremum

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