Question

Symmetrization and Contraction Principle of Random Variables

score 1k · Answer 1 · 2026-04-13 17:09:24

1k

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Symmetrization and Contraction Principle of Random Variables

Published on 13 Apr 2026 - 17:09

score 32 · Answer 2 · 2026-04-16 12:11:16

32

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Prove that $\cap_{0<p<\infty}L^p([0,1])\supset L^{\infty}([0,1])$

Published on 16 Apr 2026 - 12:11

score 73 · Answer 3 · 2026-04-15 00:52:23

73

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Prove that $\cup_{1<p\leq\infty} L^p([0,1])\subset L^1([0,1]) $.

Published on 15 Apr 2026 - 0:52

score 32 · Answer 4 · 2026-04-10 21:37:40

32

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Reference for integral equation result

Published on 10 Apr 2026 - 21:37

score 151 · Answer 5 · 2026-04-16 03:27:52

151

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If $f_n \rightarrow f$ a.e. and $\sup_n \|f_n\|_p < \infty$, then $f \in L^p$

Published on 16 Apr 2026 - 3:27

score 84 · Answer 6 · 2026-04-14 05:28:13

84

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Is $\Phi:L_p\rightarrow L_p$ continuous?

Published on 14 Apr 2026 - 5:28

score 439 · Answer 7 · 2026-04-11 06:41:00

439

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Supremum norm for convolution in sequence spaces

Published on 11 Apr 2026 - 6:41

score 46 · Answer 8 · 2026-04-16 20:48:20

46

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Example of a sequence that follows certain properties

Published on 16 Apr 2026 - 20:48

score 64 · Answer 9 · 2026-04-16 22:00:00

64

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Prove $\| \int_0^{\tau} f(s, \cdot) ds \|_p \leq \int_0^{\tau} \| f(s,\cdot) \|_p ds $

Published on 16 Apr 2026 - 22:00

score 75 · Answer 10 · 2026-04-15 19:05:07

75

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Is $L^p(\mu)$ isometrically embedded into $L^q(\mu)$ when $p=\infty$ or $q=\infty$? And what can we say about the adjoint of the embedding?

Published on 15 Apr 2026 - 19:05

score 47 · Answer 11 · 2026-04-16 06:41:56

47

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Show that $f(x)={1\over {\sqrt{x}(1+|\log x|)}}\in L^2(0,\infty)\setminus L^p(0,\infty)$ for all $p\ne 2$

Published on 16 Apr 2026 - 6:41

score 86 · Answer 12 · 2026-04-17 04:14:10

86

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$L^p$-convergence of $L^p$-bounded martingale on a countable index set

Published on 17 Apr 2026 - 4:14

score 16 · Answer 13 · 2026-04-22 02:22:02

16

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Show that $\bigcup_{t\in I}\mathcal L^p(\mathcal F_t,\text P)$ is a dense subspace of $\mathcal L^p(\mathcal F_{\sup I},\text P)$

Published on 22 Apr 2026 - 2:22

score 27 · Answer 14 · 2026-04-12 16:16:48

27

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Continuous function on $\mathbb R^n$, equipped with $||.||_{L^{\infty}(\mathbb R^n)}$

Published on 12 Apr 2026 - 16:16

score 216 · Answer 15 · 2026-04-16 02:06:41

216

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Dimension of $c/c_0$

Published on 16 Apr 2026 - 2:06

List Question

Symmetrization and Contraction Principle of Random Variables

Prove that $\cap_{0<p<\infty}L^p([0,1])\supset L^{\infty}([0,1])$

Prove that $\cup_{1<p\leq\infty} L^p([0,1])\subset L^1([0,1]) $.

Reference for integral equation result

If $f_n \rightarrow f$ a.e. and $\sup_n \|f_n\|_p < \infty$, then $f \in L^p$

Is $\Phi:L_p\rightarrow L_p$ continuous?

Supremum norm for convolution in sequence spaces

Example of a sequence that follows certain properties

Prove $\| \int_0^{\tau} f(s, \cdot) ds \|_p \leq \int_0^{\tau} \| f(s,\cdot) \|_p ds $

Is $L^p(\mu)$ isometrically embedded into $L^q(\mu)$ when $p=\infty$ or $q=\infty$? And what can we say about the adjoint of the embedding?

Show that $f(x)={1\over {\sqrt{x}(1+|\log x|)}}\in L^2(0,\infty)\setminus L^p(0,\infty)$ for all $p\ne 2$

$L^p$-convergence of $L^p$-bounded martingale on a countable index set

Show that $\bigcup_{t\in I}\mathcal L^p(\mathcal F_t,\text P)$ is a dense subspace of $\mathcal L^p(\mathcal F_{\sup I},\text P)$

Continuous function on $\mathbb R^n$, equipped with $||.||_{L^{\infty}(\mathbb R^n)}$

Dimension of $c/c_0$

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