Question

Obtain the triangle inequality from the Minkowski inequality

score 377 · Answer 1 · 2026-04-13 03:55:13

377

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Obtain the triangle inequality from the Minkowski inequality

Published on 13 Apr 2026 - 3:55

score 891 · Answer 2 · 2015-04-17 07:23:45

891

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sequence in $L^1$ converging pointwise a.e., but not weakly.

Published on 17 Apr 2015 - 7:23

score 127 · Answer 3 · 2015-04-17 09:49:12

127

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if a sequence converges in measure in $L^p$, then converging for weak topology.

Published on 17 Apr 2015 - 9:49

score 167 · Answer 4 · 2015-04-20 01:59:00

167

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$f_1,f_2 \in L^q(\mu)$ and $\int_\mathcal{X}f_1gd\mu = \int_\mathcal{X}f_2gd\mu$ for all $g \in L^p(\mu)$ implies $f_1=f_2$ a.e.

Published on 20 Apr 2015 - 1:59

score 525 · Answer 5 · 2026-04-12 23:34:36

525

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Inclusions of $\ell^p$ and $L^p$ spaces

Published on 12 Apr 2026 - 23:34

score 308 · Answer 6 · 2026-04-12 18:02:12

308

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$L^p$ spaces and proper inclusion

Published on 12 Apr 2026 - 18:02

score 89 · Answer 7 · 2015-04-21 02:05:59

89

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The $L^p$ convergence rate of the tail of the series $\sum_{n=1}^{\infty}\min\{1,2^n |x|^{-1} \}2^{-na}$

Published on 21 Apr 2015 - 2:05

score 810 · Answer 8 · 2026-04-13 11:17:56

810

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Showing that $\int fg\le \int g$ implies $f=0$ a.e.

Published on 13 Apr 2026 - 11:17

score 266 · Answer 9 · 2015-04-21 08:01:48

266

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Prove $\mathcal{L}_p[0,1]$ is separable using Lusin and Stone-Weierstrass theorems.

Published on 21 Apr 2015 - 8:01

score 732 · Answer 10 · 2026-04-13 09:02:11

732

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The Essential Supremum as a Limit

Published on 13 Apr 2026 - 9:02

score 439 · Answer 11 · 2026-03-29 02:12:33

439

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Prove that a set is orthonormal on $L_2$

Published on 29 Mar 2026 - 2:12

score 172 · Answer 12 · 2015-04-23 15:48:20

172

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On showing that if $f_n \to f, g_n \to g$ in $L^p$ then $max(f_n, g_n) \to max(f, g)$ in $L^p$

Published on 23 Apr 2015 - 15:48

score 112 · Answer 13 · 2026-04-13 01:15:55

112

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Is σ-finiteness necessary for the "in measure" version of the dominated convergence theorem to hold?

Published on 13 Apr 2026 - 1:15

score 192 · Answer 14 · 2026-04-13 00:57:29

192

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Why is the zero extension of an $L^p$ function in $L^p$?

Published on 13 Apr 2026 - 0:57

score 369 · Answer 15 · 2026-04-01 14:32:48

369

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Proof of Hunt's Interpolation

Published on 01 Apr 2026 - 14:32

List Question

Obtain the triangle inequality from the Minkowski inequality

sequence in $L^1$ converging pointwise a.e., but not weakly.

if a sequence converges in measure in $L^p$, then converging for weak topology.

$f_1,f_2 \in L^q(\mu)$ and $\int_\mathcal{X}f_1gd\mu = \int_\mathcal{X}f_2gd\mu$ for all $g \in L^p(\mu)$ implies $f_1=f_2$ a.e.

Inclusions of $\ell^p$ and $L^p$ spaces

$L^p$ spaces and proper inclusion

The $L^p$ convergence rate of the tail of the series $\sum_{n=1}^{\infty}\min\{1,2^n |x|^{-1} \}2^{-na}$

Showing that $\int fg\le \int g$ implies $f=0$ a.e.

Prove $\mathcal{L}_p[0,1]$ is separable using Lusin and Stone-Weierstrass theorems.

The Essential Supremum as a Limit

Prove that a set is orthonormal on $L_2$

On showing that if $f_n \to f, g_n \to g$ in $L^p$ then $max(f_n, g_n) \to max(f, g)$ in $L^p$

Is σ-finiteness necessary for the "in measure" version of the dominated convergence theorem to hold?

Why is the zero extension of an $L^p$ function in $L^p$?

Proof of Hunt's Interpolation

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