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A question about probability theory and a little functional analysis

score 113 · Answer 1 · 2026-04-08 20:34:26

113

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A question about probability theory and a little functional analysis

Published on 08 Apr 2026 - 20:34

score 42 · Answer 2 · 2026-04-03 00:30:57

42

Views

Proof of equivalence relation on $\mathcal{L}^p$ space

Published on 03 Apr 2026 - 0:30

score 55 · Answer 3 · 2023-11-13 13:01:45

55

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If $f$ is compactly supported and belongs to $L^{p}$ does it also belong to $L^{q}$?

Published on 13 Nov 2023 - 13:01

score 101 · Answer 4 · 2026-03-26 09:34:16

101

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If $f \in L_1(0,1)$, then $f^p \log^q (f) \in L_1(0,1)$.

Published on 26 Mar 2026 - 9:34

score 32 · Answer 5 · 2026-03-27 13:03:35

32

Views

Existence and uniqueneess of functional maximizing value on specific element of $L^p$

Published on 27 Mar 2026 - 13:03

score 45 · Answer 6 · 2023-11-15 00:46:28

45

Views

There is a function $f$ such that $f \in L^{p}$ and $f \notin L^{q}$ for $p,q \geq 1$ and $p\neq q$

Published on 15 Nov 2023 - 0:46

score 35 · Answer 7 · 2026-03-28 15:26:32

35

Views

Orthonormal Basis of $L^2[0,1]$ having indicator functions?

Published on 28 Mar 2026 - 15:26

score 204 · Answer 8 · 2023-11-18 18:52:06

204

Views

$G_p=\{\{x_n\}_{n\inℕ} \in l^p(R) :\displaystyle \sum_{k=1}^\infty x_k=0 \}$ is not closed for $p\in (1,\infty)$

Published on 18 Nov 2023 - 18:52

score 35 · Answer 9 · 2026-04-02 04:50:53

35

Views

Uniform and $L^p$ convergence of convolution with an approximate identity

Published on 02 Apr 2026 - 4:50

score 82 · Answer 10 · 2023-11-21 09:15:58

82

Views

How to prove: ${X_n}$ Uniform absolute continuous and $X_n$ Convergence in probability to $X$ equivalent to $X$ in $L_p$?

Published on 21 Nov 2023 - 9:15

score 36 · Answer 11 · 2026-04-12 00:09:47

36

Views

Solution verification of continuity of a function in $L^p(\mathbb R)$

Published on 12 Apr 2026 - 0:09

score 66 · Answer 12 · 2026-04-10 17:01:21

66

Views

Problematic duality argument in Lp space

Published on 10 Apr 2026 - 17:01

score 58 · Answer 13 · 2026-04-11 00:39:07

58

Views

Locally essentially bounded function is locally integrable

Published on 11 Apr 2026 - 0:39

score 35 · Answer 14 · 2023-11-26 10:28:02

35

Views

Convergence of a sequence in $L^2(\mathbb{R}^N)$ that is also bounded in $H^1(\mathbb{R}^N)$

Published on 26 Nov 2023 - 10:28

score 98 · Answer 15 · 2026-03-26 10:59:48

98

Views

Lebesgue spaces $\mathscr{L}^{p}$ for $p<1$

Published on 26 Mar 2026 - 10:59

List Question

A question about probability theory and a little functional analysis

Proof of equivalence relation on $\mathcal{L}^p$ space

If $f$ is compactly supported and belongs to $L^{p}$ does it also belong to $L^{q}$?

If $f \in L_1(0,1)$, then $f^p \log^q (f) \in L_1(0,1)$.

Existence and uniqueneess of functional maximizing value on specific element of $L^p$

There is a function $f$ such that $f \in L^{p}$ and $f \notin L^{q}$ for $p,q \geq 1$ and $p\neq q$

Orthonormal Basis of $L^2[0,1]$ having indicator functions?

$G_p=\{\{x_n\}_{n\inℕ} \in l^p(R) :\displaystyle \sum_{k=1}^\infty x_k=0 \}$ is not closed for $p\in (1,\infty)$

Uniform and $L^p$ convergence of convolution with an approximate identity

How to prove: ${X_n}$ Uniform absolute continuous and $X_n$ Convergence in probability to $X$ equivalent to $X$ in $L_p$?

Solution verification of continuity of a function in $L^p(\mathbb R)$

Problematic duality argument in Lp space

Locally essentially bounded function is locally integrable

Convergence of a sequence in $L^2(\mathbb{R}^N)$ that is also bounded in $H^1(\mathbb{R}^N)$

Lebesgue spaces $\mathscr{L}^{p}$ for $p<1$

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