Question

DMCT $\int fd\mu=\lim_{n\to\infty }\int f_n d\mu$ equivalent to $\lim_{n\to\infty}\int \mid f_n -f \mid d\mu=0$?

score 126 · Answer 1 · 2018-08-13 11:08:18

126

Views

DMCT $\int fd\mu=\lim_{n\to\infty }\int f_n d\mu$ equivalent to $\lim_{n\to\infty}\int \mid f_n -f \mid d\mu=0$?

Published on 13 Aug 2018 - 11:08

score 442 · Answer 2 · 2026-03-17 04:30:49

442

Views

Hölder continuity of integral function

Published on 17 Mar 2026 - 4:30

score 133 · Answer 3 · 2026-03-25 03:03:13

133

Views

Several questions about measurable functions and the sigma algebra generated by set that are symmetric around zero

Published on 25 Mar 2026 - 3:03

score 147 · Answer 4 · 2026-03-17 06:20:01

147

Views

Pushforward formula for Lebesgue Stieltjes Measure

Published on 17 Mar 2026 - 6:20

score 92 · Answer 5 · 2018-08-16 03:52:05

92

Views

A relation involving summation and integration

Published on 16 Aug 2018 - 3:52

score 90 · Answer 6 · 2018-08-16 05:35:53

90

Views

Lebesgue measure of set not equal to that of its preimage

Published on 16 Aug 2018 - 5:35

score 140 · Answer 7 · 2018-08-16 17:12:13

140

Views

Integral of an increasing function over subset of unit interval

Published on 16 Aug 2018 - 17:12

score 50 · Answer 8 · 2018-08-17 16:20:31

50

Views

Trouble with integration

Published on 17 Aug 2018 - 16:20

score 61 · Answer 9 · 2026-03-26 08:00:50

61

Views

Show that $S(x)=\sum_{n=1}^{\infty}\biggl({|\tan(n^3x)|\over{n^3}}\biggl)^{1\over2}$ converges a.e

Published on 26 Mar 2026 - 8:00

score 54 · Answer 10 · 2018-08-19 09:38:14

54

Views

Calculate $\lim_{\epsilon \rightarrow 0}{{1\over {\epsilon^2}}\cdot\biggl( 1-{1\over2}\int_{-1}^{1}}\sqrt{|1-\epsilon \cdot \sin (t)|}dt \biggl)$

Published on 19 Aug 2018 - 9:38

score 72 · Answer 11 · 2018-08-19 14:39:09

72

Views

Function in $L^1(\mathbb{R}) \cap L^2(\mathbb{R})$

Published on 19 Aug 2018 - 14:39

score 113 · Answer 12 · 2018-08-19 15:45:32

113

Views

About $f:[0,1]\rightarrow \mathbb{R}$ integrable with $f \geq 0$, and $A_{t}=\{x\in [0,1]\mid t \leq f(x) \leq 2t\}$

Published on 19 Aug 2018 - 15:45

score 166 · Answer 13 · 2018-08-20 11:23:48

166

Views

Example for Sufficiency of Conditions for Differentiating Under Lebesgue Integral

Published on 20 Aug 2018 - 11:23

score 703 · Answer 14 · 2018-08-20 16:12:05

703

Views

A question relating to uniform integrability and tightness

Published on 20 Aug 2018 - 16:12

score 67 · Answer 15 · 2018-08-20 18:17:41

67

Views

Show that $\lim_{s\rightarrow \infty} e^s m\left( f^{-1}\left([s,\infty)\right) \right) =0$.

Published on 20 Aug 2018 - 18:17

List Question

DMCT $\int fd\mu=\lim_{n\to\infty }\int f_n d\mu$ equivalent to $\lim_{n\to\infty}\int \mid f_n -f \mid d\mu=0$?

Hölder continuity of integral function

Several questions about measurable functions and the sigma algebra generated by set that are symmetric around zero

Pushforward formula for Lebesgue Stieltjes Measure

A relation involving summation and integration

Lebesgue measure of set not equal to that of its preimage

Integral of an increasing function over subset of unit interval

Trouble with integration

Show that $S(x)=\sum_{n=1}^{\infty}\biggl({|\tan(n^3x)|\over{n^3}}\biggl)^{1\over2}$ converges a.e

Calculate $\lim_{\epsilon \rightarrow 0}{{1\over {\epsilon^2}}\cdot\biggl( 1-{1\over2}\int_{-1}^{1}}\sqrt{|1-\epsilon \cdot \sin (t)|}dt \biggl)$

Function in $L^1(\mathbb{R}) \cap L^2(\mathbb{R})$

About $f:[0,1]\rightarrow \mathbb{R}$ integrable with $f \geq 0$, and $A_{t}=\{x\in [0,1]\mid t \leq f(x) \leq 2t\}$

Example for Sufficiency of Conditions for Differentiating Under Lebesgue Integral

A question relating to uniform integrability and tightness

Show that $\lim_{s\rightarrow \infty} e^s m\left( f^{-1}\left([s,\infty)\right) \right) =0$.

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