List questions from bounded-variation

Published on 14 May 2020 - 1:25

61

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A challenging problem related to characterisation on BV-functions.

Published on 26 Mar 2026 - 1:00

89

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Show that if $X$ is a bounded subset of $\textbf{R}$, then the closure $\overline{X}$ is also bounded.

Published on 16 May 2020 - 19:20

82

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Convergence of set vs convergence of perimeter

Published on 19 May 2020 - 18:01

396

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Radon measure as the derivative of a BV function

Published on 20 May 2020 - 23:12

845

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Prove that a sequence $f_n$ of functions which are bounded and converges uniformly to $f$, which is also bounded, is uniformly bounded

Published on 21 May 2020 - 0:57

115

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Prove that no function with bounded variation exists such that...

Published on 02 Jun 2020 - 15:47

217

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Proof regard to the function $ f\left(x\right)=\begin{cases} x^{2}\sin\left(\frac{1}{x^{2}}\right) & x\neq0\\ 0 & x=0 \end{cases} $

Published on 05 Jun 2020 - 20:07

329

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A function of bounded variation is bounded

Published on 11 Jun 2020 - 8:41

120

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if differentiable and derivative is bound then total variation is bounded

Published on 11 Jun 2020 - 13:06

299

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(Proof-check) Alternative formula for the total variation

Published on 11 Jun 2020 - 16:15

54

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Relation between the space of the functions that fulfill the Hölder condition and absolutely continuous functions

Published on 23 Feb 2026 - 12:07

316

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Bounded Variation Functions

Published on 20 Jun 2020 - 23:16

248

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Convergence of BV functions

Published on 24 Jun 2020 - 12:04

41

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Question About BPV function

Published on 05 Jul 2020 - 10:12

List Question

How do we prove that uniform convergence preserves boundedness?

A challenging problem related to characterisation on BV-functions.

Show that if $X$ is a bounded subset of $\textbf{R}$, then the closure $\overline{X}$ is also bounded.

Convergence of set vs convergence of perimeter

Radon measure as the derivative of a BV function

Prove that a sequence $f_n$ of functions which are bounded and converges uniformly to $f$, which is also bounded, is uniformly bounded

Prove that no function with bounded variation exists such that...

Proof regard to the function $ f\left(x\right)=\begin{cases} x^{2}\sin\left(\frac{1}{x^{2}}\right) & x\neq0\\ 0 & x=0 \end{cases} $

A function of bounded variation is bounded

if differentiable and derivative is bound then total variation is bounded

(Proof-check) Alternative formula for the total variation

Relation between the space of the functions that fulfill the Hölder condition and absolutely continuous functions

Bounded Variation Functions

Convergence of BV functions

Question About BPV function

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