List questions from bounded-variation

Published on 31 Oct 2019 - 11:40

957

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pointwise convergent sequence of bounded variation functions

Published on 23 Feb 2026 - 21:34

81

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Understanding an example on section 6.3 in Royden 4th edition on pg.117.

Published on 10 Nov 2019 - 4:06

54

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Understanding the proof of lemma 5 on pg.117 in Royden and Fitzpatrick 4th edition.

Published on 10 Nov 2019 - 20:15

459

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Show that a total variation is greater or equal than absolute value of a function

Published on 13 Nov 2019 - 18:56

66

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If $g(x)$ is strictly increasing, then $g(x)+ah(x)$ is also strictly increasing for some small positive constant $a$?

Published on 26 Nov 2019 - 20:31

246

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Bounded Variation Function and its Total Variation

Published on 25 Mar 2026 - 6:30

489

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Why $BV[a,b]$ is not separable?

Published on 07 Dec 2019 - 6:13

143

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Show that $|\mu|$ is the smallest of those positive measures $\nu$ that satisfy $|\mu(A)| \le \nu(A)$.

Published on 16 Dec 2019 - 23:02

96

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$\lim\limits_{n\rightarrow\infty}T(f-f_n)=0$.($T$:total variation, $f_n$: absolutely continuous). Then $f$ is absolutely continuous.

Published on 23 Feb 2026 - 8:34

270

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What is the exact connection between BV-Functions and their weak derivatives

Published on 26 Mar 2026 - 4:31

188

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Integration by parts VS fundamental theorem of calculus

Published on 23 Feb 2026 - 8:32

157

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$BV$-functions and trace.

Published on 08 Jan 2020 - 19:36

92

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Find a minimizer of an operator on $BV$-space

Published on 08 Jan 2020 - 19:50

41

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Show that $f(x, y) = x^3 y^{- 2} e^{- x^2 / y}$ is smooth, and unbounded near the origin

Published on 11 Jan 2020 - 15:45

List Question

Expectation of a finite variation integral

pointwise convergent sequence of bounded variation functions

Understanding an example on section 6.3 in Royden 4th edition on pg.117.

Understanding the proof of lemma 5 on pg.117 in Royden and Fitzpatrick 4th edition.

Show that a total variation is greater or equal than absolute value of a function

If $g(x)$ is strictly increasing, then $g(x)+ah(x)$ is also strictly increasing for some small positive constant $a$?

Bounded Variation Function and its Total Variation

Why $BV[a,b]$ is not separable?

Show that $|\mu|$ is the smallest of those positive measures $\nu$ that satisfy $|\mu(A)| \le \nu(A)$.

$\lim\limits_{n\rightarrow\infty}T(f-f_n)=0$.($T$:total variation, $f_n$: absolutely continuous). Then $f$ is absolutely continuous.

What is the exact connection between BV-Functions and their weak derivatives

Integration by parts VS fundamental theorem of calculus

$BV$-functions and trace.

Find a minimizer of an operator on $BV$-space

Show that $f(x, y) = x^3 y^{- 2} e^{- x^2 / y}$ is smooth, and unbounded near the origin

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