Question

Absolute Continuity and $\sigma$-finiteness

score 239 · Answer 1 · 2016-11-15 14:07:19

239

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Absolute Continuity and $\sigma$-finiteness

Published on 15 Nov 2016 - 14:07

score 386 · Answer 2 · 2016-11-16 05:05:23

386

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question related to Lipschitz continuous function

Published on 16 Nov 2016 - 5:05

score 275 · Answer 3 · 2016-11-28 02:31:59

275

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Let $f$ be monotonic increasing on $[a,b]$ If $\int_a^bf'(x)dx = f(b)-f(a)$ Show $f$ is absolutely continuous

Published on 28 Nov 2016 - 2:31

score 219 · Answer 4 · 2016-12-07 19:06:28

219

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Prove that $ \frac{d\nu}{d\lambda}=\frac{d\nu}{d\mu}\cdot \frac{d\mu}{d\lambda},\text{ } \lambda\text{-a.e.} $

Published on 07 Dec 2016 - 19:06

score 104 · Answer 5 · 2016-12-10 17:11:46

104

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How to find a function which has bouned variaion but is not absolutely continuous

Published on 10 Dec 2016 - 17:11

score 34 · Answer 6 · 2016-12-11 18:33:20

34

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$f(x)=\mu([a,x]\cap E )$. Calculate $f'$

Published on 11 Dec 2016 - 18:33

score 611 · Answer 7 · 2016-12-13 23:13:08

611

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Continuous function with derivative a.e. and Luzin N property is absolutely continuous

Published on 13 Dec 2016 - 23:13

score 96 · Answer 8 · 2016-12-18 15:53:49

96

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Confused about a step of a proof using absolute continuity...

Published on 18 Dec 2016 - 15:53

score 211 · Answer 9 · 2016-12-19 10:42:24

211

Views

Show a property for open intervals of absolute continuous functions

Published on 19 Dec 2016 - 10:42

score 889 · Answer 10 · 2016-12-28 03:24:14

889

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Prove that if $f:[0,1] \to \mathbb{R}$ is absolutely continuous, then $|f|^p$ is absolutely continuous for $p>1$

Published on 28 Dec 2016 - 3:24

score 73 · Answer 11 · 2017-01-01 16:08:37

73

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Show that $ \mu_n \to \mu $, in the weak* topology, where $ \mu \ll \nu $ and $ \dfrac{d\mu }{d\nu}=\dfrac{f}{\|f\|_1} $

Published on 01 Jan 2017 - 16:08

score 295 · Answer 12 · 2017-01-05 02:34:57

295

Views

Lebesgue measure on $L^2$

Published on 05 Jan 2017 - 2:34

score 195 · Answer 13 · 2017-01-22 09:40:46

195

Views

Absolute continuity of a function defined by an integral as $f(x)=\int_{0}^{g(x)}h'(t)dt$

Published on 22 Jan 2017 - 9:40

score 266 · Answer 14 · 2017-01-23 10:19:16

266

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Textbook on absolute continuity

Published on 23 Jan 2017 - 10:19

score 56 · Answer 15 · 2017-01-23 18:12:28

56

Views

How strong continuity is needed for the values of derivative on rational numbers to contain all information about the derivative?

Published on 23 Jan 2017 - 18:12

List Question

Absolute Continuity and $\sigma$-finiteness

question related to Lipschitz continuous function

Let $f$ be monotonic increasing on $[a,b]$ If $\int_a^bf'(x)dx = f(b)-f(a)$ Show $f$ is absolutely continuous

Prove that $ \frac{d\nu}{d\lambda}=\frac{d\nu}{d\mu}\cdot \frac{d\mu}{d\lambda},\text{ } \lambda\text{-a.e.} $

How to find a function which has bouned variaion but is not absolutely continuous

$f(x)=\mu([a,x]\cap E )$. Calculate $f'$

Continuous function with derivative a.e. and Luzin N property is absolutely continuous

Confused about a step of a proof using absolute continuity...

Show a property for open intervals of absolute continuous functions

Prove that if $f:[0,1] \to \mathbb{R}$ is absolutely continuous, then $|f|^p$ is absolutely continuous for $p>1$

Show that $ \mu_n \to \mu $, in the weak* topology, where $ \mu \ll \nu $ and $ \dfrac{d\mu }{d\nu}=\dfrac{f}{\|f\|_1} $

Lebesgue measure on $L^2$

Absolute continuity of a function defined by an integral as $f(x)=\int_{0}^{g(x)}h'(t)dt$

Textbook on absolute continuity

How strong continuity is needed for the values of derivative on rational numbers to contain all information about the derivative?

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