Question

Closure of subset of $\ell^\infty$

score 150 · Answer 1 · 2026-04-14 02:38:29

150

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Closure of subset of $\ell^\infty$

Published on 14 Apr 2026 - 2:38

score 984 · Answer 2 · 2026-04-12 20:24:21

984

Views

When is the space $L^\infty(\mu)$ finite-dimensional?

Published on 12 Apr 2026 - 20:24

score 113 · Answer 3 · 2026-04-13 03:42:59

113

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How can I find a function that is in $L^1(\mathbb{R})$ with its derivative also but its limit tends to zero?

Published on 13 Apr 2026 - 3:42

score 2.3k · Answer 4 · 2026-04-13 19:51:45

2.3k

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Does $\{\sin (nx)\}_1^\infty$ converge in the $L^1$ norm on $[0,2\pi]$?

Published on 13 Apr 2026 - 19:51

score 2.9k · Answer 5 · 2026-04-16 17:57:54

2.9k

Views

$L^p$ convergence of a bounded sequence which converges almost everywhere

Published on 16 Apr 2026 - 17:57

score 113 · Answer 6 · 2026-04-16 00:17:11

113

Views

Example of $\{f_n\}$ which converges to $f(x)\equiv0$ in $L^ 1$ , but so that $f_n(x)\not\to0$ in $[0, 1]$.

Published on 16 Apr 2026 - 0:17

score 88 · Answer 7 · 2026-04-15 20:09:32

88

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If $f_n\to f$ in the $L^1$ norm, show that there is a subsequence $f_{n_k}$ which converges a.e. to $f$.

Published on 15 Apr 2026 - 20:09

score 2k · Answer 8 · 2026-04-16 08:51:40

2k

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Give an example of a function which is in $L^2 (\mathbb{R})$ but not in $L^p(\mathbb{R})$ for any $p \in [1, 2) \cup (2, \infty]$.

Published on 16 Apr 2026 - 8:51

score 1.5k · Answer 9 · 2026-04-17 03:57:22

1.5k

Views

Show that the set of functions in $L^2[0,1]$ with a zero integral on $[0,1]$ is a closed vector subspace of $L^2[0,1]$.

Published on 17 Apr 2026 - 3:57

score 126 · Answer 10 · 2026-04-13 13:59:48

126

Views

Are Morrey spaces reflexive?

Published on 13 Apr 2026 - 13:59

score 34 · Answer 11 · 2026-04-13 14:04:10

34

Views

Minimize the uniform ($L^\infty$) distance to the space of functions with zero integral

Published on 13 Apr 2026 - 14:04

score 629 · Answer 12 · 2026-04-11 11:36:59

629

Views

Nowhere dense subset of $L^1$

Published on 11 Apr 2026 - 11:36

score 2.3k · Answer 13 · 2026-04-12 18:53:25

2.3k

Views

Relation between Besov and Sobolev spaces (Littlewood-Paley-theory)

Published on 12 Apr 2026 - 18:53

score 19 · Answer 14 · 2026-04-15 16:39:55

19

Views

Proving equivalence of operators imply equivalence of measures

Published on 15 Apr 2026 - 16:39

score 214 · Answer 15 · 2015-12-02 16:03:15

214

Views

Why $L^p$ is strictly contained in $L^{p,\infty}$

Published on 02 Dec 2015 - 16:03

List Question

Closure of subset of $\ell^\infty$

When is the space $L^\infty(\mu)$ finite-dimensional?

How can I find a function that is in $L^1(\mathbb{R})$ with its derivative also but its limit tends to zero?

Does $\{\sin (nx)\}_1^\infty$ converge in the $L^1$ norm on $[0,2\pi]$?

$L^p$ convergence of a bounded sequence which converges almost everywhere

Example of $\{f_n\}$ which converges to $f(x)\equiv0$ in $L^ 1$ , but so that $f_n(x)\not\to0$ in $[0, 1]$.

If $f_n\to f$ in the $L^1$ norm, show that there is a subsequence $f_{n_k}$ which converges a.e. to $f$.

Give an example of a function which is in $L^2 (\mathbb{R})$ but not in $L^p(\mathbb{R})$ for any $p \in [1, 2) \cup (2, \infty]$.

Show that the set of functions in $L^2[0,1]$ with a zero integral on $[0,1]$ is a closed vector subspace of $L^2[0,1]$.

Are Morrey spaces reflexive?

Minimize the uniform ($L^\infty$) distance to the space of functions with zero integral

Nowhere dense subset of $L^1$

Relation between Besov and Sobolev spaces (Littlewood-Paley-theory)

Proving equivalence of operators imply equivalence of measures

Why $L^p$ is strictly contained in $L^{p,\infty}$

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