List questions from absolute-continuity

Published on 04 Nov 2022 - 18:42

47

Views

Finding a set $E$, $m(E)=0$, such that $m(f(E))>0$ where f is a continuous but not absolutely continuous function.

Published on 05 Nov 2022 - 16:18

97

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Is it possible to show that an absolutely continuous function $I\to \mathbb{R}$ is differentiable a.e. without invoking Lebesgue theory?

Published on 07 Nov 2022 - 21:25

143

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Preimage of a null set by a non-monotonic absolutely continuous function

Published on 19 Nov 2022 - 23:07

722

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If the Riemann-Stieltjes integral $\int_a^b{f\,dg}$ exists for every $f\in\mathcal{R}[a,b]$, then $g$ is absolutely continuous

Published on 24 Nov 2022 - 4:09

190

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Absolutely continuous curves in Wasserstein distance and measurability.

Published on 23 Feb 2026 - 12:04

41

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An absolutely continuous function has bounded variation

Published on 27 Dec 2022 - 3:00

65

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Is this a sloppy point in a proof of a theorem about absolute continuity?

Published on 27 Dec 2022 - 4:13

91

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If $f$ is absolutely continuous and $f' = 0$ $\lambda$-a.e., then $f$ is constant

Published on 03 Jan 2023 - 10:22

61

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Let $f \in L_1 (\lambda)$ and $F(x) := \int_a^x f \mathrm d \lambda$. Then $F$ is absolutely continuous

Published on 03 Jan 2023 - 10:50

103

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A characterization of absolutely continuous functions

Published on 03 Jan 2023 - 13:29

34

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Function in $AC$ but not in $KC^1$

Published on 12 Jan 2023 - 13:13

131

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Radon-Nikodym derivative with respect to product of marginal measures

Published on 19 Jan 2023 - 16:46

780

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Why do we write $P\ll Q$ and why is $P$ called absolutely continuous w.r.t. $Q$?

Published on 21 Jan 2023 - 15:48

List Question

Product measure and absolute continuity.

Finding a set $E$, $m(E)=0$, such that $m(f(E))>0$ where f is a continuous but not absolutely continuous function.

Is it possible to show that an absolutely continuous function $I\to \mathbb{R}$ is differentiable a.e. without invoking Lebesgue theory?

Preimage of a null set by a non-monotonic absolutely continuous function

If the Riemann-Stieltjes integral $\int_a^b{f\,dg}$ exists for every $f\in\mathcal{R}[a,b]$, then $g$ is absolutely continuous

Absolutely continuous curves in Wasserstein distance and measurability.

An absolutely continuous function has bounded variation

Is this a sloppy point in a proof of a theorem about absolute continuity?

If $f$ is absolutely continuous and $f' = 0$ $\lambda$-a.e., then $f$ is constant

Let $f \in L_1 (\lambda)$ and $F(x) := \int_a^x f \mathrm d \lambda$. Then $F$ is absolutely continuous

A characterization of absolutely continuous functions

Function in $AC$ but not in $KC^1$

Radon-Nikodym derivative with respect to product of marginal measures

Why do we write $P\ll Q$ and why is $P$ called absolutely continuous w.r.t. $Q$?

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