Question

It is true for a continuous differentiable bounded function $f(x)$ that its total variation $V_a^b(f)\ge\max_{a<x<b}f(x)-\min_{a<x<b}f(x)$?

score 109 · Answer 1 · 2026-03-25 17:52:09

109

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It is true for a continuous differentiable bounded function $f(x)$ that its total variation $V_a^b(f)\ge\max_{a<x<b}f(x)-\min_{a<x<b}f(x)$?

Published on 25 Mar 2026 - 17:52

score 52 · Answer 2 · 2026-03-27 18:43:15

52

Views

Lipschitz function without Lipschitz-like increments

Published on 27 Mar 2026 - 18:43

score 646 · Answer 3 · 2021-10-03 15:04:00

646

Views

Show that $BV([a,b])$ is a Banach space

Published on 03 Oct 2021 - 15:04

score 63 · Answer 4 · 2026-03-28 02:14:42

63

Views

Increments of Lipschitz function do not satisfy an operator bound

Published on 28 Mar 2026 - 2:14

score 81 · Answer 5 · 2021-10-05 14:03:10

81

Views

Lipschitz does not bound increments by 1-variation

Published on 05 Oct 2021 - 14:03

score 68 · Answer 6 · 2026-02-24 09:50:40

68

Views

Jordan decomposition of differentiable functions

Published on 24 Feb 2026 - 9:50

score 122 · Answer 7 · 2026-03-25 17:39:28

122

Views

Total Variation of a Borel Measure vs Total Variation of a Function

Published on 25 Mar 2026 - 17:39

score 70 · Answer 8 · 2021-11-04 09:23:23

70

Views

Construct counterexamples regarding bounded variation function

Published on 04 Nov 2021 - 9:23

score 36 · Answer 9 · 2026-03-25 15:41:07

36

Views

Compact immersions of the bounded variation space $BV(\Omega)$

Published on 25 Mar 2026 - 15:41

score 120 · Answer 10 · 2021-11-07 14:33:17

120

Views

Prove that there exist $M$ such that when $|h|$ is sufficiently small, $ \frac{1}{h}\int_a^b|f(x+h)-f(x)|\mathrm{d}x\leq M. $

Published on 07 Nov 2021 - 14:33

score 62 · Answer 11 · 2026-02-26 04:19:31

62

Views

Does boundedness in $L^\infty ( 0,T; L^1 (\Omega))$ imply boundedness in $L^\infty (0,T;BV(\Omega))$?

Published on 26 Feb 2026 - 4:19

score 56 · Answer 12 · 2026-03-25 17:52:07

56

Views

Variation of g, $\Vert f \Vert$, being less than variation of $\hat g$ on page 49 of Schechter's Principle of Functional Analysis

Published on 25 Mar 2026 - 17:52

score 268 · Answer 13 · 2021-11-18 15:23:46

268

Views

Is $BV$ the dual of a separable Banach space?

Published on 18 Nov 2021 - 15:23

score 149 · Answer 14 · 2021-11-23 11:37:13

149

Views

Can I split $E$ in equal volume parts?

Published on 23 Nov 2021 - 11:37

score 69 · Answer 15 · 2021-12-03 09:09:23

69

Views

bounded variation functions on $[0,1]$ are always $L_2[0,1]$?

Published on 03 Dec 2021 - 9:09

List Question

It is true for a continuous differentiable bounded function $f(x)$ that its total variation $V_a^b(f)\ge\max_{a<x<b}f(x)-\min_{a<x<b}f(x)$?

Lipschitz function without Lipschitz-like increments

Show that $BV([a,b])$ is a Banach space

Increments of Lipschitz function do not satisfy an operator bound

Lipschitz does not bound increments by 1-variation

Jordan decomposition of differentiable functions

Total Variation of a Borel Measure vs Total Variation of a Function

Construct counterexamples regarding bounded variation function

Compact immersions of the bounded variation space $BV(\Omega)$

Prove that there exist $M$ such that when $|h|$ is sufficiently small, $ \frac{1}{h}\int_a^b|f(x+h)-f(x)|\mathrm{d}x\leq M. $

Does boundedness in $L^\infty ( 0,T; L^1 (\Omega))$ imply boundedness in $L^\infty (0,T;BV(\Omega))$?

Variation of g, $\Vert f \Vert$, being less than variation of $\hat g$ on page 49 of Schechter's Principle of Functional Analysis

Is $BV$ the dual of a separable Banach space?

Can I split $E$ in equal volume parts?

bounded variation functions on $[0,1]$ are always $L_2[0,1]$?

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