Question

$\int gf \, d \lambda = 0$ for all continuous $g$ implies $f=0$ almost surely"

score 217 · Answer 1 · 2026-04-15 21:07:14

217

Views

$\int gf \, d \lambda = 0$ for all continuous $g$ implies $f=0$ almost surely"

Published on 15 Apr 2026 - 21:07

score 57 · Answer 2 · 2026-04-16 21:01:36

57

Views

Show that $\left. \frac{d}{dp}\right|_{p=1} \left[ \int f^p \, d\mu \right]^{1/p} =\int f \log(f) \, d\mu$

Published on 16 Apr 2026 - 21:01

score 81 · Answer 3 · 2026-04-16 00:36:44

81

Views

$\int_{\Bbb{T}} e_n(\lambda) |\varphi(\lambda)|^2 = 0$ for all $n \neq 0$ implies $|\varphi|^2$ is constant almost surely

Published on 16 Apr 2026 - 0:36

score 551 · Answer 4 · 2026-04-15 06:50:10

551

Views

Help me understand and compute a Fréchet derivative in $L^2$

Published on 15 Apr 2026 - 6:50

score 47 · Answer 5 · 2026-04-01 10:36:02

47

Views

Which space is $L^1(\partial\Omega)$?

Published on 01 Apr 2026 - 10:36

score 65 · Answer 6 · 2026-04-14 22:53:40

65

Views

Is there a continuous embedding of $W^{k,\:p}(A)$ into $W^{k,\:p}(B)$ for all open $A,B\subseteq\mathbb R^d$ with $A\subseteq B$?

Published on 14 Apr 2026 - 22:53

score 623 · Answer 7 · 2026-04-16 20:02:47

623

Views

Proving $L^q(\mathbb{T}) \subseteq L^p(\mathbb{T})$ for $1 \leq p < q \leq \infty$

Published on 16 Apr 2026 - 20:02

score 44 · Answer 8 · 2026-04-12 13:12:14

44

Views

What does "extension by approximation" mean?

Published on 12 Apr 2026 - 13:12

score 719 · Answer 9 · 2026-04-11 05:38:08

719

Views

Swapping $L^p$ norm and integral

Published on 11 Apr 2026 - 5:38

score 46 · Answer 10 · 2026-04-11 19:18:18

46

Views

Proving two equivalent statement that come from Otto Holder's theorem

Published on 11 Apr 2026 - 19:18

score 131 · Answer 11 · 2026-04-16 13:27:15

131

Views

$L^1$ convergence of $p$-bounded functions is $p-bounded$

Published on 16 Apr 2026 - 13:27

score 201 · Answer 12 · 2026-04-11 18:21:07

201

Views

compact operator between $L^{p}(\mu)$ and $C(X)$

Published on 11 Apr 2026 - 18:21

score 56 · Answer 13 · 2026-04-15 07:23:22

56

Views

If a sequence is in $\ell_p$, then it's also in $\ell_{p'}$ for all $p'\ge p$

Published on 15 Apr 2026 - 7:23

score 143 · Answer 14 · 2026-04-30 10:23:03

143

Views

Does uniform convergence of a subsequence imply uniform convergence of the sequence? If so, how to show this?

Published on 30 Apr 2026 - 10:23

score 683 · Answer 15 · 2026-04-14 22:18:29

683

Views

How to prove $L^{\infty}(\mathbb R) \cap L^{1} (\mathbb R) \subset L^{2}(\mathbb R)$

Published on 14 Apr 2026 - 22:18

List Question

$\int gf \, d \lambda = 0$ for all continuous $g$ implies $f=0$ almost surely"

Show that $\left. \frac{d}{dp}\right|_{p=1} \left[ \int f^p \, d\mu \right]^{1/p} =\int f \log(f) \, d\mu$

$\int_{\Bbb{T}} e_n(\lambda) |\varphi(\lambda)|^2 = 0$ for all $n \neq 0$ implies $|\varphi|^2$ is constant almost surely

Help me understand and compute a Fréchet derivative in $L^2$

Which space is $L^1(\partial\Omega)$?

Is there a continuous embedding of $W^{k,\:p}(A)$ into $W^{k,\:p}(B)$ for all open $A,B\subseteq\mathbb R^d$ with $A\subseteq B$?

Proving $L^q(\mathbb{T}) \subseteq L^p(\mathbb{T})$ for $1 \leq p < q \leq \infty$

What does "extension by approximation" mean?

Swapping $L^p$ norm and integral

Proving two equivalent statement that come from Otto Holder's theorem

$L^1$ convergence of $p$-bounded functions is $p-bounded$

compact operator between $L^{p}(\mu)$ and $C(X)$

If a sequence is in $\ell_p$, then it's also in $\ell_{p'}$ for all $p'\ge p$

Does uniform convergence of a subsequence imply uniform convergence of the sequence? If so, how to show this?

How to prove $L^{\infty}(\mathbb R) \cap L^{1} (\mathbb R) \subset L^{2}(\mathbb R)$

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