Question

A question about measure of symmetric difference of sets

score 216 · Answer 1 · 2019-03-26 04:38:33

A question about measure of symmetric difference of sets

Published on 26 Mar 2019 - 4:38

score 355 · Answer 2 · 2019-03-28 03:11:02

$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.

score 33 · Answer 3 · 2026-03-25 20:42:28

33

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$E=L^1(\Bbb R) \Rightarrow E'=L^{\infty}(\Bbb R) \Rightarrow E''\ne L^1(\Bbb R) $

Published on 25 Mar 2026 - 20:42

score 89 · Answer 4 · 2019-03-28 17:04:52

89

Views

How do I conclude from $ f \notin L^{p}$ that $f_{n} \nrightarrow f$ in $L^{p}$

Published on 28 Mar 2019 - 17:04

score 138 · Answer 5 · 2019-03-28 17:39:52

138

Views

Are $L^{1}(\mathbb{R)}$ and $L^{1}((0,1))$ isometric?

Published on 28 Mar 2019 - 17:39

score 34 · Answer 6 · 2019-03-29 07:08:33

34

Views

$\int_{\mathbb R^d} (1+ |x-n|^2)^{s} |f(x)|^2 dx = \sum_{k\in \mathbb Z^d}(1+ |k-n|^2)^s \int_{I_k}|f(x)|^2 dx?$

Published on 29 Mar 2019 - 7:08

score 53 · Answer 7 · 2019-03-30 00:23:47

53

Views

A question about Schwartz space

Published on 30 Mar 2019 - 0:23

score 110 · Answer 8 · 2026-03-26 01:28:03

110

Views

An example of a function in weighted Lipschitz class but not in Lipschitz class

Published on 26 Mar 2026 - 1:28

score 169 · Answer 9 · 2026-03-25 06:26:25

169

Views

A generalized Hölder inequality

Published on 25 Mar 2026 - 6:26

score 196 · Answer 10 · 2026-03-26 15:17:17

196

Views

Identification between von Neumann algebras and measure spaces

Published on 26 Mar 2026 - 15:17

score 58 · Answer 11 · 2026-03-30 04:27:56

58

Views

Series expansion of expectation

Published on 30 Mar 2026 - 4:27

score 41 · Answer 12 · 2019-04-01 04:45:09

41

Views

Prove $||f||_p\leq(\beta-\alpha)^{\frac{1}{p}-\frac{1}{q}}||f||_q$.

Published on 01 Apr 2019 - 4:45

score 100 · Answer 13 · 2019-04-02 03:36:50

100

Views

Noncompactness of $L^{p}$ space in $[-1,1]$ interval

Published on 02 Apr 2019 - 3:36

score 127 · Answer 14 · 2026-03-29 14:03:30

127

Views

$f_n(x) \to f(x)$ and $\int |f_n|^2 \, d\mu \to \int |f|^2 \, d\mu$. Use Egorov's theorem to show $f_n \to f$ in $L^2(d\mu)$.

Published on 29 Mar 2026 - 14:03

score 352 · Answer 15 · 2026-03-26 01:09:24

352

Views

Showing the multiplication operator only has closed range for characteristic functions

Published on 26 Mar 2026 - 1:09

List Question

A question about measure of symmetric difference of sets

$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.

$E=L^1(\Bbb R) \Rightarrow E'=L^{\infty}(\Bbb R) \Rightarrow E''\ne L^1(\Bbb R) $

How do I conclude from $ f \notin L^{p}$ that $f_{n} \nrightarrow f$ in $L^{p}$

Are $L^{1}(\mathbb{R)}$ and $L^{1}((0,1))$ isometric?

$\int_{\mathbb R^d} (1+ |x-n|^2)^{s} |f(x)|^2 dx = \sum_{k\in \mathbb Z^d}(1+ |k-n|^2)^s \int_{I_k}|f(x)|^2 dx?$

A question about Schwartz space

An example of a function in weighted Lipschitz class but not in Lipschitz class

A generalized Hölder inequality

Identification between von Neumann algebras and measure spaces

Series expansion of expectation

Prove $||f||_p\leq(\beta-\alpha)^{\frac{1}{p}-\frac{1}{q}}||f||_q$.

Noncompactness of $L^{p}$ space in $[-1,1]$ interval

$f_n(x) \to f(x)$ and $\int |f_n|^2 \, d\mu \to \int |f|^2 \, d\mu$. Use Egorov's theorem to show $f_n \to f$ in $L^2(d\mu)$.

Showing the multiplication operator only has closed range for characteristic functions

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