Question

Bounded variation implies supremum over all partitions is finite. What if we impose that the bound depends on the partition?

score 377 · Answer 1 · 2020-03-25 17:24:04

377

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Bounded variation implies supremum over all partitions is finite. What if we impose that the bound depends on the partition?

Published on 25 Mar 2020 - 17:24

score 80 · Answer 2 · 2026-03-25 17:41:53

80

Views

(Proof) $g\in BV[a,b]$ and $f\in\mathcal{R}_g[a,b]$ and $f$ bounded $\Rightarrow 1/f\in\mathcal{R}_g[a,b]$

Published on 25 Mar 2026 - 17:41

score 67 · Answer 3 · 2020-03-31 16:18:48

67

Views

Let $f\in BV([a,b])$ then $|f|\in BV([a,b])$

Published on 31 Mar 2020 - 16:18

score 35 · Answer 4 · 2020-04-12 11:26:47

35

Views

Is bounded variation function monotonic in a small neighborhood?

Published on 12 Apr 2020 - 11:26

score 253 · Answer 5 · 2020-04-13 15:41:23

253

Views

Are integral functions of continuous functions of bounded variation?

Published on 13 Apr 2020 - 15:41

score 152 · Answer 6 · 2026-03-26 03:18:40

152

Views

To find class K infinity bounds on given radially unbounded function

Published on 26 Mar 2026 - 3:18

score 1k · Answer 7 · 2020-04-21 18:26:16

1k

Views

Calculate total variation on $[0,2\pi]$ of $f(x)$

Published on 21 Apr 2020 - 18:26

score 540 · Answer 8 · 2020-04-26 23:52:29

540

Views

Show that any finite subset of $\textbf{R}$ is closed an bounded.

Published on 26 Apr 2020 - 23:52

score 61 · Answer 9 · 2020-04-30 08:15:13

61

Views

Exercise 1.2.5 from Chung's "A Course in Probability Theory"

Published on 30 Apr 2020 - 8:15

score 122 · Answer 10 · 2020-04-30 23:51:33

122

Views

Let $f:X\rightarrow\textbf{R}$ be a uniformly continuous function. Suppose that $E$ is a bounded subset of $X$. Then $f(E)$ is also bounded.

Published on 30 Apr 2020 - 23:51

score 115 · Answer 11 · 2026-02-23 10:20:30

115

Views

Let $f:[a,b]\to \mathbb{R}$ be differentiable everywhere on $(a,b)$ and has an integrable derivative, is f absolutely continuous?

Published on 23 Feb 2026 - 10:20

score 375 · Answer 12 · 2026-03-25 19:05:53

375

Views

Inequality about functions of bounded variation and Riemann-Stieltjes integrals

Published on 25 Mar 2026 - 19:05

score 32 · Answer 13 · 2020-05-11 07:04:21

32

Views

A theorem on bounded variation-proof.

Published on 11 May 2020 - 7:04

score 138 · Answer 14 · 2020-05-12 11:43:27

138

Views

Bounded Variate function and its total variation has different points of differentiabilty

Published on 12 May 2020 - 11:43

score 105 · Answer 15 · 2020-05-12 21:55:26

105

Views

If $I$ and $J$ are bounded intervals, then the intersection $I\cap J$ is also a bounded interval.

Published on 12 May 2020 - 21:55

List Question

Bounded variation implies supremum over all partitions is finite. What if we impose that the bound depends on the partition?

(Proof) $g\in BV[a,b]$ and $f\in\mathcal{R}_g[a,b]$ and $f$ bounded $\Rightarrow 1/f\in\mathcal{R}_g[a,b]$

Let $f\in BV([a,b])$ then $|f|\in BV([a,b])$

Is bounded variation function monotonic in a small neighborhood?

Are integral functions of continuous functions of bounded variation?

To find class K infinity bounds on given radially unbounded function

Calculate total variation on $[0,2\pi]$ of $f(x)$

Show that any finite subset of $\textbf{R}$ is closed an bounded.

Exercise 1.2.5 from Chung's "A Course in Probability Theory"

Let $f:X\rightarrow\textbf{R}$ be a uniformly continuous function. Suppose that $E$ is a bounded subset of $X$. Then $f(E)$ is also bounded.

Let $f:[a,b]\to \mathbb{R}$ be differentiable everywhere on $(a,b)$ and has an integrable derivative, is f absolutely continuous?

Inequality about functions of bounded variation and Riemann-Stieltjes integrals

A theorem on bounded variation-proof.

Bounded Variate function and its total variation has different points of differentiabilty

If $I$ and $J$ are bounded intervals, then the intersection $I\cap J$ is also a bounded interval.

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