Question

Existence of functions $g, h:[a,b]\rightarrow \mathbb{R}$ such that f = g / h

score 49 · Answer 1 · 2026-04-15 22:17:16

49

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Existence of functions $g, h:[a,b]\rightarrow \mathbb{R}$ such that f = g / h

Published on 15 Apr 2026 - 22:17

score 1.2k · Answer 2 · 2026-05-10 16:58:08

1.2k

Views

Positive and negative variation

Published on 10 May 2026 - 16:58

score 63 · Answer 3 · 2026-04-15 15:07:35

63

Views

$\frac{\partial f}{\partial x_{i}}$ is bounded variation implies $ f\in L^{\frac{n}{n-1}}\left(\Omega\right). $

Published on 15 Apr 2026 - 15:07

score 512 · Answer 4 · 2026-04-09 06:49:06

512

Views

Examples about bounded variation function

Published on 09 Apr 2026 - 6:49

score 208 · Answer 5 · 2026-03-25 11:02:20

208

Views

perimeter of sets. How do $P(E,\Omega)$ and $P(E\cap \Omega,\mathbb{R}^n)$ relate?

Published on 25 Mar 2026 - 11:02

score 45 · Answer 6 · 2026-04-15 05:16:17

45

Views

Sustainable population - When to breed

Published on 15 Apr 2026 - 5:16

score 99 · Answer 7 · 2026-04-17 12:35:02

99

Views

Suppose $\sum_{n=1}^{\infty} V(f_n - f;a,b) < \infty$, prove that $f_n^{'}$ converges almost everywhere to $f^{'}$

Published on 17 Apr 2026 - 12:35

score 392 · Answer 8 · 2026-04-11 17:56:30

392

Views

Certain Set of Functions with Bounded Variation is Compact

Published on 11 Apr 2026 - 17:56

score 199 · Answer 9 · 2026-04-13 17:22:38

199

Views

Is a continuous function with derivative zero a.e. of bounded variation?

Published on 13 Apr 2026 - 17:22

score 1k · Answer 10 · 2026-04-14 04:34:05

1k

Views

$f$ is continuous and of bounded variation on $[a,b]$, then $V[a,x]$ is continuous?

Published on 14 Apr 2026 - 4:34

score 527 · Answer 11 · 2026-04-10 11:56:40

527

Views

Probability Function and Bounded Variation Function

Published on 10 Apr 2026 - 11:56

score 229 · Answer 12 · 2026-04-15 04:09:27

229

Views

Show $f(x) = x^2 \sin (x^{-3/2}), x\in (0,1] $, $f(0) = 0$ is of bounded variation without using improper integral

Published on 15 Apr 2026 - 4:09

score 70 · Answer 13 · 2026-04-15 23:00:54

Show if $ V_0^1(f, P) \le \sum_{i=1}^n (2c_i + \frac{3}{2\sqrt{c_i}}) (x_i - x_{i-1}), \forall P \in P[0,1]$ then $f$ is of bounded variation

score 125 · Answer 14 · 2026-04-12 08:00:02

125

Views

Explanation of Proof of Theorem 6.1 of Chapter II of The Laplace Transform by Widder

Published on 12 Apr 2026 - 8:00

score 610 · Answer 15 · 2026-04-09 22:59:51

610

Views

Complex Borel Measure and Bounded Variation Functions

Published on 09 Apr 2026 - 22:59

List Question

Existence of functions $g, h:[a,b]\rightarrow \mathbb{R}$ such that f = g / h

Positive and negative variation

$\frac{\partial f}{\partial x_{i}}$ is bounded variation implies $ f\in L^{\frac{n}{n-1}}\left(\Omega\right). $

Examples about bounded variation function

perimeter of sets. How do $P(E,\Omega)$ and $P(E\cap \Omega,\mathbb{R}^n)$ relate?

Sustainable population - When to breed

Suppose $\sum_{n=1}^{\infty} V(f_n - f;a,b) < \infty$, prove that $f_n^{'}$ converges almost everywhere to $f^{'}$

Certain Set of Functions with Bounded Variation is Compact

Is a continuous function with derivative zero a.e. of bounded variation?

$f$ is continuous and of bounded variation on $[a,b]$, then $V[a,x]$ is continuous?

Probability Function and Bounded Variation Function

Show $f(x) = x^2 \sin (x^{-3/2}), x\in (0,1] $, $f(0) = 0$ is of bounded variation without using improper integral

Show if $ V_0^1(f, P) \le \sum_{i=1}^n (2c_i + \frac{3}{2\sqrt{c_i}}) (x_i - x_{i-1}), \forall P \in P[0,1]$ then $f$ is of bounded variation

Explanation of Proof of Theorem 6.1 of Chapter II of The Laplace Transform by Widder

Complex Borel Measure and Bounded Variation Functions

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