List questions from absolute-continuity

Published on 13 Nov 2019 - 20:51

129

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Why are the functions inside the integral integrable?

Published on 17 Nov 2019 - 0:35

22

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Is the following set a set of increasing absolutely continuous functions?

Published on 08 Dec 2019 - 10:03

1.4k

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Showing that space of absolutely continuous functions is Banach space

Published on 12 Dec 2019 - 13:34

560

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Pointwise convergent, increasing sequence

Published on 13 Dec 2019 - 0:58

373

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A measurable function $F$ sends measurable sets to measurable sets $\iff$ it has the Luzin n property. (In $R$)

Published on 19 Dec 2019 - 2:23

159

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Countable $\sigma$-finite measure dominated by a probability measure

Published on 25 Dec 2019 - 8:52

171

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Is the regular conditional probability of $\mathbb P$ dominated by $\mathbb P$ almost surely?

Published on 26 Dec 2019 - 5:47

95

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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 01 Jan 2020 - 0:43

187

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Integration by parts VS fundamental theorem of calculus

Published on 04 Jan 2020 - 14:41

337

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Show that $f(x)$ is absolutely continuous in $[0,1]$, but not for $|f|^{1/2}(x)$.

Published on 14 Jan 2020 - 1:01

111

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Weaker ACL property if only one weak derivative, with respect to one variable, exists?

Published on 27 Jan 2020 - 7:16

41

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Why is the measure $\nu$ nonnegative here?

Published on 27 Jan 2020 - 17:18

191

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Is it true that the continuous $2\pi$-periodic function is almost everywhere differentiable?

Published on 05 Feb 2020 - 5:49

50

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Integrals of partial derivative

Published on 17 Feb 2020 - 10:14

List Question

Equivalent norms on $AC([a,b])$

Why are the functions inside the integral integrable?

Is the following set a set of increasing absolutely continuous functions?

Showing that space of absolutely continuous functions is Banach space

Pointwise convergent, increasing sequence

A measurable function $F$ sends measurable sets to measurable sets $\iff$ it has the Luzin n property. (In $R$)

Countable $\sigma$-finite measure dominated by a probability measure

Is the regular conditional probability of $\mathbb P$ dominated by $\mathbb P$ almost surely?

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

Integration by parts VS fundamental theorem of calculus

Show that $f(x)$ is absolutely continuous in $[0,1]$, but not for $|f|^{1/2}(x)$.

Weaker ACL property if only one weak derivative, with respect to one variable, exists?

Why is the measure $\nu$ nonnegative here?

Is it true that the continuous $2\pi$-periodic function is almost everywhere differentiable?

Integrals of partial derivative

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