Question

Integrability of a square of an integral

score 68 · Answer 1 · 2017-11-13 20:52:43

68

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Integrability of a square of an integral

Published on 13 Nov 2017 - 20:52

score 117 · Answer 2 · 2017-11-21 17:20:01

117

Views

Convergence of the Lebesgue-Stieltjes measures induced by pointwise convergent functions of bounded variation

Published on 21 Nov 2017 - 17:20

score 479 · Answer 3 · 2026-02-23 10:21:48

479

Views

Riemann Stieltjes integral. Prove that $\lim_{|P| \to 0} S(f,P,T) = \int_a^bfd\alpha$

Published on 23 Feb 2026 - 10:21

score 73 · Answer 4 · 2017-11-23 23:42:22

If the variation of a measure $μ$ is smaller than the variation of a measure $ν$ on any compact interval, then $μ$ is absolutely continuous wrt $ν$

score 4.3k · Answer 5 · 2017-11-28 03:46:50

4.3k

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bounded $\implies$ integrable?

Published on 28 Nov 2017 - 3:46

score 52 · Answer 6 · 2026-02-23 10:19:34

52

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Bounded variation of $\frac1f$ when $\inf(|f|)>0$ & $f$ bounded variation

Published on 23 Feb 2026 - 10:19

score 651 · Answer 7 · 2026-03-25 13:13:33

651

Views

The old and modern definitions of total variation are actually equivalent?

Published on 25 Mar 2026 - 13:13

score 256 · Answer 8 · 2017-12-01 03:45:35

256

Views

Every polynomial $p(x)$ is of boundary variation in the interval $[a,b]$ and $V_a^b p \leq \int_a^b \vert p'(s) ds \vert$

Published on 01 Dec 2017 - 3:45

score 539 · Answer 9 · 2026-03-25 13:04:57

539

Views

When the total variation of a function equals the integral of its gradient

Published on 25 Mar 2026 - 13:04

score 85 · Answer 10 · 2026-03-25 13:13:22

85

Views

On searching conditions, other than the continuity of $f,$ under which $ \lim_{\mu (P) \rightarrow 0} V(f,P) = V_a^b f $ is also valid.

Published on 25 Mar 2026 - 13:13

score 606 · Answer 11 · 2017-12-12 22:05:41

606

Views

Understdanding the definition of the perimeter of a set

Published on 12 Dec 2017 - 22:05

score 56 · Answer 12 · 2017-12-19 19:07:57

56

Views

Bounded function of variation

Published on 19 Dec 2017 - 19:07

score 462 · Answer 13 · 2017-12-21 21:52:45

462

Views

Structure of Caccioppoli sets

Published on 21 Dec 2017 - 21:52

score 185 · Answer 14 · 2018-01-04 14:09:06

185

Views

On weak-star convergence of functions and almost everywhere convergence of derivatives

Published on 04 Jan 2018 - 14:09

score 1.4k · Answer 15 · 2026-03-26 03:11:30

1.4k

Views

Riemann-Stieltjes Integral with respect to total variation

Published on 26 Mar 2026 - 3:11

List Question

Integrability of a square of an integral

Convergence of the Lebesgue-Stieltjes measures induced by pointwise convergent functions of bounded variation

Riemann Stieltjes integral. Prove that $\lim_{|P| \to 0} S(f,P,T) = \int_a^bfd\alpha$

If the variation of a measure $μ$ is smaller than the variation of a measure $ν$ on any compact interval, then $μ$ is absolutely continuous wrt $ν$

bounded $\implies$ integrable?

Bounded variation of $\frac1f$ when $\inf(|f|)>0$ & $f$ bounded variation

The old and modern definitions of total variation are actually equivalent?

Every polynomial $p(x)$ is of boundary variation in the interval $[a,b]$ and $V_a^b p \leq \int_a^b \vert p'(s) ds \vert$

When the total variation of a function equals the integral of its gradient

On searching conditions, other than the continuity of $f,$ under which $ \lim_{\mu (P) \rightarrow 0} V(f,P) = V_a^b f $ is also valid.

Understdanding the definition of the perimeter of a set

Bounded function of variation

Structure of Caccioppoli sets

On weak-star convergence of functions and almost everywhere convergence of derivatives

Riemann-Stieltjes Integral with respect to total variation

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