Question

The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm

score 8.3k · Answer 1 · 2026-04-14 14:31:54

8.3k

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The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm

Published on 14 Apr 2026 - 14:31

score 102 · Answer 2 · 2026-04-11 16:06:52

102

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Integral of an integrable, measurable function over sets of measure converging to zero

Published on 11 Apr 2026 - 16:06

score 80 · Answer 3 · 2026-04-16 20:56:47

80

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$f \mapsto \int f^2$ is $L^1$-weakly lower semicontinuous

Published on 16 Apr 2026 - 20:56

score 8.8k · Answer 4 · 2026-04-14 16:29:40

8.8k

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Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.

Published on 14 Apr 2026 - 16:29

score 1.9k · Answer 5 · 2026-04-25 08:53:35

1.9k

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Compactness of Sobolev Space in L infinity

Published on 25 Apr 2026 - 8:53

score 92 · Answer 6 · 2026-04-15 12:41:39

92

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Did B[0,1] is a closed subspace of $L^2[0,1]$

Published on 15 Apr 2026 - 12:41

score 242 · Answer 7 · 2026-04-09 03:16:18

242

Views

Surjectivity of the transpose of an operator

Published on 09 Apr 2026 - 3:16

score 1.8k · Answer 8 · 2026-04-12 15:33:42

1.8k

Views

Convergence in measure and bounded $L^p$ norm implies convergence in $L^p$

Published on 12 Apr 2026 - 15:33

score 183 · Answer 9 · 2026-04-11 19:17:50

183

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Interpolation of Lp spaces - help with understanding a part of a proof

Published on 11 Apr 2026 - 19:17

score 399 · Answer 10 · 2026-04-13 06:38:36

399

Views

Closed infinite dimensional linear subspace of $L^p((0,1))$ consisting of continuous functions

Published on 13 Apr 2026 - 6:38

score 86 · Answer 11 · 2026-04-14 01:31:31

86

Views

Proving inequalities on $L^P$ spaces

Published on 14 Apr 2026 - 1:31

score 150 · Answer 12 · 2026-04-10 07:57:00

150

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Understanding convergence in $L^P$ ( Through a counter example )

Published on 10 Apr 2026 - 7:57

score 108 · Answer 13 · 2026-04-16 17:52:55

108

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$\int_0^1 f(x)dx \times \int_0^1{\frac{1}{f(x)}}dx \geq 1$

Published on 16 Apr 2026 - 17:52

score 905 · Answer 14 · 2026-04-15 12:02:33

905

Views

Reverse of Holder's Inequality

Published on 15 Apr 2026 - 12:02

score 285 · Answer 15 · 2026-04-16 08:50:22

285

Views

Proving that $L^p \cap L^{\infty} \supset L^r$ where $1 \leq p <r < \infty$

Published on 16 Apr 2026 - 8:50

List Question

The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm

Integral of an integrable, measurable function over sets of measure converging to zero

$f \mapsto \int f^2$ is $L^1$-weakly lower semicontinuous

Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.

Compactness of Sobolev Space in L infinity

Did B[0,1] is a closed subspace of $L^2[0,1]$

Surjectivity of the transpose of an operator

Convergence in measure and bounded $L^p$ norm implies convergence in $L^p$

Interpolation of Lp spaces - help with understanding a part of a proof

Closed infinite dimensional linear subspace of $L^p((0,1))$ consisting of continuous functions

Proving inequalities on $L^P$ spaces

Understanding convergence in $L^P$ ( Through a counter example )

$\int_0^1 f(x)dx \times \int_0^1{\frac{1}{f(x)}}dx \geq 1$

Reverse of Holder's Inequality

Proving that $L^p \cap L^{\infty} \supset L^r$ where $1 \leq p <r < \infty$

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