List questions from absolute-continuity

Published on 01 Jun 2018 - 14:50

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$f: [0,1] \to \mathbb{R}$ absolutely continuous, $f' \in \{0,1\}$ (a.e.), $f(0)=0$. Prove that for some measurable subset $A$, $f(x)=m(A \cap (0,x))$

Published on 23 Jun 2018 - 14:54

387

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Prove that $f$ is absolutely continuous.

Published on 03 Jul 2018 - 21:25

459

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Differentiability of a singleton set

Published on 13 Jul 2018 - 10:28

351

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If total variation function for f of bounded variation is absolutely continuous, then f is absolutely continuous

Published on 21 Jul 2018 - 21:19

121

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$x \sin({1 \over x})$ can be decomposed?

Published on 28 Jul 2018 - 20:07

330

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Does absolute convergence imply integrability?

Published on 06 Aug 2018 - 6:07

102

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differentiability of variation of absolutely continuous function

Published on 10 Aug 2018 - 11:54

440

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Hölder continuity of integral function

Published on 14 Aug 2018 - 16:43

1k

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$\{f_n\}$ absolutely continuous converging pointwise to $f$. Is $f$ of bounded variation and/or absolutely continuous?

Published on 07 Sep 2018 - 10:27

431

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A question about absolute continuity

Published on 16 Sep 2018 - 1:29

887

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Absolutely continuous and differentiable almost everywhere

Published on 20 Sep 2018 - 18:21

49

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Regularity in the trapezoidal rule

Published on 02 Oct 2018 - 19:22

89

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$T_{f}(a,x)$ is absolutely continuous in $[a,b]$ whenever $f$ is absolutely continuous $[a,b]$. (Proof verification)

Published on 20 Oct 2018 - 18:43

95

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Why the Lemma below is true even if the measure $\mu$ is infinite?

Published on 31 Oct 2018 - 0:47

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Show measure zero: application of Theorem 1 in Lang (1986)?

$f: [0,1] \to \mathbb{R}$ absolutely continuous, $f' \in \{0,1\}$ (a.e.), $f(0)=0$. Prove that for some measurable subset $A$, $f(x)=m(A \cap (0,x))$

Prove that $f$ is absolutely continuous.

Differentiability of a singleton set

If total variation function for f of bounded variation is absolutely continuous, then f is absolutely continuous

$x \sin({1 \over x})$ can be decomposed?

Does absolute convergence imply integrability?

differentiability of variation of absolutely continuous function

Hölder continuity of integral function

$\{f_n\}$ absolutely continuous converging pointwise to $f$. Is $f$ of bounded variation and/or absolutely continuous?

A question about absolute continuity

Absolutely continuous and differentiable almost everywhere

Regularity in the trapezoidal rule

$T_{f}(a,x)$ is absolutely continuous in $[a,b]$ whenever $f$ is absolutely continuous $[a,b]$. (Proof verification)

Why the Lemma below is true even if the measure $\mu$ is infinite?

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