Question

Sum of absolutely continuous functions is absolutely continuous

score 1.3k · Answer 1 · 2017-08-30 21:15:19

1.3k

Views

Sum of absolutely continuous functions is absolutely continuous

Published on 30 Aug 2017 - 21:15

score 604 · Answer 2 · 2017-09-01 00:05:58

604

Views

The definition of absolute continuity without disjointness of intervals is satisfied only by Lipschitz functions

Published on 01 Sep 2017 - 0:05

score 574 · Answer 3 · 2017-09-14 08:32:10

574

Views

Can we identify absolutely continuous functions on $(a,b)$ with values in $X$ with $W^{1,1}((a,b);X)$?

Published on 14 Sep 2017 - 8:32

score 752 · Answer 4 · 2017-09-20 02:39:37

752

Views

Absolute continuity of Lebesgue integral for $L^2$ function

Published on 20 Sep 2017 - 2:39

score 222 · Answer 5 · 2017-09-22 08:59:29

222

Views

$f ' \in L^1(\mathbb{R})$ implies absolute continuity of $f$ on some subset of $\Omega$

Published on 22 Sep 2017 - 8:59

score 348 · Answer 6 · 2017-10-09 18:15:59

348

Views

If $f$ is absolutely continuous and $g$ is continuous, prove $f' =g$.

Published on 09 Oct 2017 - 18:15

score 402 · Answer 7 · 2017-10-22 23:50:20

402

Views

Integral representation of convex function

Published on 22 Oct 2017 - 23:50

score 24 · Answer 8 · 2017-10-24 17:21:38

24

Views

$\lim_{h \to 0} \frac{f(x+hy,y)-f(x,y)}{h} = g(x,y)$ in $L^1$ norm implies absolute continuity of $f(\cdot,y)$ with $yf_x'(x,y) = g(x,y)$

Published on 24 Oct 2017 - 17:21

score 1.5k · Answer 9 · 2017-10-26 20:15:35

1.5k

Views

Absolutely continuous representative of Sobolev function

Published on 26 Oct 2017 - 20:15

score 324 · Answer 10 · 2017-11-02 02:18:10

324

Views

The function $f(x)=x \sin(1/x), f(0)=0$ has the Luzin N property

Published on 02 Nov 2017 - 2:18

score 78 · Answer 11 · 2017-11-14 02:25:26

78

Views

Question mark function not absolutely continuous

Published on 14 Nov 2017 - 2:25

score 2k · Answer 12 · 2017-11-14 17:42:29

2k

Views

is the space of absolutely continuous functions complete

Published on 14 Nov 2017 - 17:42

score 410 · Answer 13 · 2017-11-14 20:52:35

410

Views

absolutely continuous functions as a subspace of continuous functions with bounded variation

Published on 14 Nov 2017 - 20:52

score 70 · Answer 14 · 2017-11-17 14:09:26

70

Views

Continuous injection between AC and C

Published on 17 Nov 2017 - 14:09

score 164 · Answer 15 · 2017-11-24 19:15:34

164

Views

Can a uniformly continuous derivative fail to be absolutely continuous?

Published on 24 Nov 2017 - 19:15

List Question

Sum of absolutely continuous functions is absolutely continuous

The definition of absolute continuity without disjointness of intervals is satisfied only by Lipschitz functions

Can we identify absolutely continuous functions on $(a,b)$ with values in $X$ with $W^{1,1}((a,b);X)$?

Absolute continuity of Lebesgue integral for $L^2$ function

$f ' \in L^1(\mathbb{R})$ implies absolute continuity of $f$ on some subset of $\Omega$

If $f$ is absolutely continuous and $g$ is continuous, prove $f' =g$.

Integral representation of convex function

$\lim_{h \to 0} \frac{f(x+hy,y)-f(x,y)}{h} = g(x,y)$ in $L^1$ norm implies absolute continuity of $f(\cdot,y)$ with $yf_x'(x,y) = g(x,y)$

Absolutely continuous representative of Sobolev function

The function $f(x)=x \sin(1/x), f(0)=0$ has the Luzin N property

Question mark function not absolutely continuous

is the space of absolutely continuous functions complete

absolutely continuous functions as a subspace of continuous functions with bounded variation

Continuous injection between AC and C

Can a uniformly continuous derivative fail to be absolutely continuous?

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