Question

Deducing weak convergence of $f_n$ s.t for every $g \in L^q(\mu)$, $\lim_n \int f_n g \,d\mu$ converges

score 62 · Answer 1 · 2026-04-17 10:15:51

62

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Deducing weak convergence of $f_n$ s.t for every $g \in L^q(\mu)$, $\lim_n \int f_n g \,d\mu$ converges

Published on 17 Apr 2026 - 10:15

score 72 · Answer 2 · 2026-04-13 15:58:18

72

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bounded variation functions on $[0,1]$ are always $L_2[0,1]$?

Published on 13 Apr 2026 - 15:58

score 118 · Answer 3 · 2026-04-12 20:50:13

118

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A Question on Epsilon-Delta Proofs in Measure Theory

Published on 12 Apr 2026 - 20:50

score 69 · Answer 4 · 2026-04-14 18:39:21

69

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Show $f$ is in $L^p$ given Markov-like inequality

Published on 14 Apr 2026 - 18:39

score 42 · Answer 5 · 2026-04-15 18:34:11

42

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Multiplying $\ell^\alpha$ elements by $n^\varepsilon$

Published on 15 Apr 2026 - 18:34

score 385 · Answer 6 · 2026-04-15 04:10:26

385

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When is $L^{p}\left(\Omega \right)$ a Hilbert space?

Published on 15 Apr 2026 - 4:10

score 63 · Answer 7 · 2026-04-13 16:19:30

63

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Convergence in $L_2$ implies convergence in $L_1$.

Published on 13 Apr 2026 - 16:19

score 95 · Answer 8 · 2026-05-06 06:54:07

95

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Convergence uniformly in $\mathbb{R}$, but not in $L^{2}(\mathbb{R})$, and convergence in $L^{2}(\mathbb{R})$, but not uniformly in $\mathbb{R}$

Published on 06 May 2026 - 6:54

score 238 · Answer 9 · 2026-04-18 15:35:18

238

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Necessary and sufficient conditions for weak convergence in $L^p(0,1)$, $1<p <\infty$

Published on 18 Apr 2026 - 15:35

score 117 · Answer 10 · 2026-04-14 17:21:51

117

Views

Prove convergence in $L^1$ if norms in $L^2$ are uniformly bounded

Published on 14 Apr 2026 - 17:21

score 53 · Answer 11 · 2026-04-16 15:32:31

53

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Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Published on 16 Apr 2026 - 15:32

score 81 · Answer 12 · 2026-05-14 09:57:05

81

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Is it true that $f\in L^1(\mathbb R)$ and $(1+x^2)f''\in L^1(\mathbb R)$ imply $xf'\in L^1(\mathbb R)$?

Published on 14 May 2026 - 9:57

score 67 · Answer 13 · 2026-04-15 03:42:54

67

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Dual of $L^1[a,b]$ is $L^{\infty}[a,b]$

Published on 15 Apr 2026 - 3:42

score 97 · Answer 14 · 2026-04-16 04:48:33

97

Views

For which $p \in [1, \infty]$ the sequence is Cauchy

Published on 16 Apr 2026 - 4:48

score 79 · Answer 15 · 2026-04-13 18:12:56

79

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$f$ is a square-integrable function, $ \|f(x+h)-f(x)\|_{L^2}=O(h^{1+\alpha}), h\rightarrow 0. $

Published on 13 Apr 2026 - 18:12

List Question

Deducing weak convergence of $f_n$ s.t for every $g \in L^q(\mu)$, $\lim_n \int f_n g \,d\mu$ converges

bounded variation functions on $[0,1]$ are always $L_2[0,1]$?

A Question on Epsilon-Delta Proofs in Measure Theory

Show $f$ is in $L^p$ given Markov-like inequality

Multiplying $\ell^\alpha$ elements by $n^\varepsilon$

When is $L^{p}\left(\Omega \right)$ a Hilbert space?

Convergence in $L_2$ implies convergence in $L_1$.

Convergence uniformly in $\mathbb{R}$, but not in $L^{2}(\mathbb{R})$, and convergence in $L^{2}(\mathbb{R})$, but not uniformly in $\mathbb{R}$

Necessary and sufficient conditions for weak convergence in $L^p(0,1)$, $1<p <\infty$

Prove convergence in $L^1$ if norms in $L^2$ are uniformly bounded

Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Is it true that $f\in L^1(\mathbb R)$ and $(1+x^2)f''\in L^1(\mathbb R)$ imply $xf'\in L^1(\mathbb R)$?

Dual of $L^1[a,b]$ is $L^{\infty}[a,b]$

For which $p \in [1, \infty]$ the sequence is Cauchy

$f$ is a square-integrable function, $ \|f(x+h)-f(x)\|_{L^2}=O(h^{1+\alpha}), h\rightarrow 0. $

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