Question

Show the following measure theory result.

score 34 · Answer 1 · 2018-05-02 20:45:40

34

Views

Show the following measure theory result.

Published on 02 May 2018 - 20:45

score 23 · Answer 2 · 2026-03-25 15:43:42

23

Views

Trying to show $\mathcal S(\Bbb R)\subset L^p(\Bbb R)\ \forall 1\leq p\leq\infty$

Published on 25 Mar 2026 - 15:43

score 77 · Answer 3 · 2018-05-03 19:14:52

77

Views

Equality between integrable functions on a probability space and improper Riemann integral

Published on 03 May 2018 - 19:14

score 81 · Answer 4 · 2026-03-25 15:47:04

81

Views

A sequence in $L^p$ which converges weakly to zero but not strongly.

Published on 25 Mar 2026 - 15:47

score 338 · Answer 5 · 2018-05-05 03:06:37

338

Views

Durett Exercise 1.7.1, applying Fubini's theorem

Published on 05 May 2018 - 3:06

score 131 · Answer 6 · 2018-05-05 10:42:20

131

Views

Equivalent assertions regarding an almost everywhere zero function on Lebesgue measure space

Published on 05 May 2018 - 10:42

score 153 · Answer 7 · 2026-03-24 23:52:27

153

Views

Does there exist a measurable function with a specific property?

Published on 24 Mar 2026 - 23:52

score 38 · Answer 8 · 2018-05-06 02:42:23

38

Views

Checking if a function induces a measure, and if it does, calculating an explicit integral

Published on 06 May 2018 - 2:42

score 93 · Answer 9 · 2026-03-25 12:54:55

93

Views

$\displaystyle\lim_{\varepsilon\to 0}f\ast\varphi_{\varepsilon}(x)=f(x)$

Published on 25 Mar 2026 - 12:54

score 554 · Answer 10 · 2018-05-07 09:12:54

554

Views

Decay rate of least eigenvalue of Gram matrices.

Published on 07 May 2018 - 9:12

score 339 · Answer 11 · 2018-05-07 09:27:34

339

Views

Why I cannot use Beppo-Levi theorem here?

Published on 07 May 2018 - 9:27

score 50 · Answer 12 · 2018-05-07 15:49:50

50

Views

What is the difference between $L^1$ and $\mathcal L^1$?

Published on 07 May 2018 - 15:49

score 444 · Answer 13 · 2018-05-07 18:31:31

444

Views

$f:(0,1)\rightarrow \mathbb{R}$ given by $f(x)=\frac{1}{x}\sin(\frac{1}{x})$ is not Lebesgue integrable.

Published on 07 May 2018 - 18:31

score 249 · Answer 14 · 2018-05-08 00:55:10

249

Views

Egoroff's theorem and integrability?

Published on 08 May 2018 - 0:55

score 355 · Answer 15 · 2018-05-08 01:17:45

355

Views

Let $f:\mathbb{R}\rightarrow[0,\infty]$ be measurable that $\int f(x)dx=0$, then $f(x)=0$ for a.e.

Published on 08 May 2018 - 1:17

List Question

Show the following measure theory result.

Trying to show $\mathcal S(\Bbb R)\subset L^p(\Bbb R)\ \forall 1\leq p\leq\infty$

Equality between integrable functions on a probability space and improper Riemann integral

A sequence in $L^p$ which converges weakly to zero but not strongly.

Durett Exercise 1.7.1, applying Fubini's theorem

Equivalent assertions regarding an almost everywhere zero function on Lebesgue measure space

Does there exist a measurable function with a specific property?

Checking if a function induces a measure, and if it does, calculating an explicit integral

$\displaystyle\lim_{\varepsilon\to 0}f\ast\varphi_{\varepsilon}(x)=f(x)$

Decay rate of least eigenvalue of Gram matrices.

Why I cannot use Beppo-Levi theorem here?

What is the difference between $L^1$ and $\mathcal L^1$?

$f:(0,1)\rightarrow \mathbb{R}$ given by $f(x)=\frac{1}{x}\sin(\frac{1}{x})$ is not Lebesgue integrable.

Egoroff's theorem and integrability?

Let $f:\mathbb{R}\rightarrow[0,\infty]$ be measurable that $\int f(x)dx=0$, then $f(x)=0$ for a.e.

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