List questions from absolute-continuity

Published on 22 Feb 2026 - 20:03

132

Views

Doe this imply absolute continuity?

Published on 22 Feb 2026 - 19:50

445

Views

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

Published on 22 Feb 2026 - 19:53

648

Views

Function composition: $\Phi$ locally Lipschitz map and $f \in AC([0,1])$

Published on 22 Feb 2026 - 19:49

43

Views

Convergence almost surely/in probability

Published on 22 Feb 2026 - 19:47

2.2k

Views

Conterexample for Product of Absolutely Continuous Functions is Absolutely Continous

Published on 22 Feb 2026 - 19:52

731

Views

Absolute continuity of a Borel measure

Published on 22 Feb 2026 - 19:55

459

Views

Do singular distributions have any real-world applications?

Published on 22 Feb 2026 - 19:49

219

Views

Variation on Lipschitz continuity condition

Published on 22 Feb 2026 - 19:47

71

Views

If $\lim_{k \rightarrow \infty} g_k(x)=g(x) \text{, and } \lim_{k \rightarrow \infty} g_k^{'}(x)=f(x) \text{ a.e.}$ show $g^{'}(x)=f(x) \text{ a.e.}$

Published on 22 Feb 2026 - 19:54

1.9k

Views

If $f$ is absolutely continuous and $f'(x) = 0$ a.e., then $f$ is constant

Published on 22 Feb 2026 - 19:53

319

Views

$f:[a,b]\to[c,d]$ is absolutely continuous and bijective. Is $f^{-1}$ of bounded variation? Does $m(E) = 0$ imply $m(f(E))=0$?

Published on 22 Feb 2026 - 21:31

60

Views

$A propriety of a given fuction

Published on 22 Feb 2026 - 21:29

667

Views

Sufficient conditions for probability measure of singleton sets being zero

Published on 22 Feb 2026 - 21:28

57

Views

Implications of assumptions on the distribution and support of a random vector

Published on 22 Feb 2026 - 21:32

List Question

Absolutely continuous functions are dense in $L^1$

Doe this imply absolute continuity?

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

Function composition: $\Phi$ locally Lipschitz map and $f \in AC([0,1])$

Convergence almost surely/in probability

Conterexample for Product of Absolutely Continuous Functions is Absolutely Continous

Absolute continuity of a Borel measure

Do singular distributions have any real-world applications?

Variation on Lipschitz continuity condition

If $\lim_{k \rightarrow \infty} g_k(x)=g(x) \text{, and } \lim_{k \rightarrow \infty} g_k^{'}(x)=f(x) \text{ a.e.}$ show $g^{'}(x)=f(x) \text{ a.e.}$

If $f$ is absolutely continuous and $f'(x) = 0$ a.e., then $f$ is constant

$f:[a,b]\to[c,d]$ is absolutely continuous and bijective. Is $f^{-1}$ of bounded variation? Does $m(E) = 0$ imply $m(f(E))=0$?

$A propriety of a given fuction

Sufficient conditions for probability measure of singleton sets being zero

Implications of assumptions on the distribution and support of a random vector

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