List questions from lp-spaces

Published on 31 Mar 2026 - 13:15

123

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$L^\infty$ convergence does not imply uniform convergence almost everywhere

Published on 25 Mar 2026 - 13:53

299

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Dual space of $\ell_{1}$ is $\ell_{\infty}$

Published on 26 Mar 2026 - 18:57

596

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L1 convergence of convolution with an almost mollifier

Published on 29 Mar 2026 - 20:27

105

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On the definition of $L^p$-bounded martingales.

Published on 31 Mar 2026 - 5:15

103

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Showing whether an $L^\infty$ function is in $L^2$

Published on 10 Jan 2020 - 19:09

152

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Finding the spectrum of a compact operator

Published on 29 Mar 2026 - 12:12

98

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Norm of a bounded functional

Published on 11 Jan 2020 - 20:33

40

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Belonging to an $ L^p$ space...

Published on 11 Jan 2020 - 22:15

85

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$X\in L_1$ then $\lim\limits_{x\to\infty} \int\limits_{{|X|>x}} XdP =0$

Published on 12 Jan 2020 - 21:59

242

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How to show convergence of this sequence in $L^2?$

Published on 02 Apr 2026 - 10:54

5.1k

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In regard to $L^p$ spaces, is $L^p \subset L^q$ for $p<q$?

Published on 01 Apr 2026 - 17:28

78

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Show that $\left\{ f_{n}\right\} _{n=1}^{\infty}$ converges to $f$ in $L^{p}$, i.e., $\left|\left|f_{n}-f\right|\right|_{p}\to0$.

Published on 14 Jan 2020 - 3:13

29

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Exercise about convergence for RVs

Published on 24 Feb 2026 - 2:10

115

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Proving an Inequality in the $L^1$-Norm by Density of $C^{\infty}_{0}$

Published on 16 Jan 2020 - 10:59

List Question

If $f$ and $\operatorname{sign}(f)\in L^2([0,1])$, is $f\in L^1([0,1])$?

$L^\infty$ convergence does not imply uniform convergence almost everywhere

Dual space of $\ell_{1}$ is $\ell_{\infty}$

L1 convergence of convolution with an almost mollifier

On the definition of $L^p$-bounded martingales.

Showing whether an $L^\infty$ function is in $L^2$

Finding the spectrum of a compact operator

Norm of a bounded functional

Belonging to an $ L^p$ space...

$X\in L_1$ then $\lim\limits_{x\to\infty} \int\limits_{{|X|>x}} XdP =0$

How to show convergence of this sequence in $L^2?$

In regard to $L^p$ spaces, is $L^p \subset L^q$ for $p<q$?

Show that $\left\{ f_{n}\right\} _{n=1}^{\infty}$ converges to $f$ in $L^{p}$, i.e., $\left|\left|f_{n}-f\right|\right|_{p}\to0$.

Exercise about convergence for RVs

Proving an Inequality in the $L^1$-Norm by Density of $C^{\infty}_{0}$

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