Question

How to show that $L^p$ norm is monotone increasing?

score 10.9k · Answer 1 · 2026-04-11 20:14:09

10.9k

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How to show that $L^p$ norm is monotone increasing?

Published on 11 Apr 2026 - 20:14

score 471 · Answer 2 · 2026-04-15 17:49:42

471

Views

On the space $L^0$ and $\lim_{p \to 0} \|f\|_p$

Published on 15 Apr 2026 - 17:49

score 588 · Answer 3 · 2026-04-15 18:12:55

588

Views

Weak $L^p$ implies strong $L^q$ for $q<p$

Published on 15 Apr 2026 - 18:12

score 1.3k · Answer 4 · 2026-04-17 10:34:58

1.3k

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For what $p$ is $\frac{1}{(x(1+\ln(x)^2))^p}$ Lebesgue integrable?

Published on 17 Apr 2026 - 10:34

score 67 · Answer 5 · 2026-04-14 13:07:01

67

Views

Show that $\mu(f)\mu(1/f)\geq\mu(\Omega)^2$

Published on 14 Apr 2026 - 13:07

score 40 · Answer 6 · 2026-04-16 09:39:28

40

Views

How to arrive at the answer $x_k= a^{-\frac{1}{p}}$?

Published on 16 Apr 2026 - 9:39

score 162 · Answer 7 · 2026-04-13 22:00:01

162

Views

Metric-space complete?

Published on 13 Apr 2026 - 22:00

score 89 · Answer 8 · 2026-04-17 11:02:17

89

Views

$\left \| \left \| f \right \|_{L^{p}} \right \|_{L^{q}} \leq \left \| \left \| f \right \|_{L^{q}} \right \|_{L^{p}} $ for $0<p\leq q$

Published on 17 Apr 2026 - 11:02

score 68 · Answer 9 · 2026-04-10 19:42:18

68

Views

Pointwise boundedness implies function included in $L^\infty$?

Published on 10 Apr 2026 - 19:42

score 86 · Answer 10 · 2026-04-12 05:52:31

86

Views

Conditions to ensure nice integrability of supremum of difference on neighborhood

Published on 12 Apr 2026 - 5:52

score 528 · Answer 11 · 2026-04-17 02:03:57

528

Views

$L^2(\mathbb{R})$ sequence such that $\sum_{n=1}^{\infty}\int_{\mathbb{R}}f_n(x)g(x)d\mu(x)=0$

Published on 17 Apr 2026 - 2:03

score 721 · Answer 12 · 2026-04-15 13:42:50

721

Views

Suppose $\mu$ is a finite measure on the Borel sets of $R$ such that $f(x) = \int_R f(x + t) \mu(dt)$ a.e., show $\mu(\{0\}) = 1$.

Published on 15 Apr 2026 - 13:42

score 155 · Answer 13 · 2026-04-09 05:29:05

155

Views

Does $(\ell^{1}(\mathbb Z), \cdot)$ have a bounded approximate identity?

Published on 09 Apr 2026 - 5:29

score 114 · Answer 14 · 2026-04-15 05:27:56

114

Views

Convergence in $L^2$ on $C([0,1])$ implies convergence in $L^1$.

Published on 15 Apr 2026 - 5:27

score 274 · Answer 15 · 2026-03-28 23:57:54

274

Views

Integrability of Riesz potential

Published on 28 Mar 2026 - 23:57

List Question

How to show that $L^p$ norm is monotone increasing?

On the space $L^0$ and $\lim_{p \to 0} \|f\|_p$

Weak $L^p$ implies strong $L^q$ for $q<p$

For what $p$ is $\frac{1}{(x(1+\ln(x)^2))^p}$ Lebesgue integrable?

Show that $\mu(f)\mu(1/f)\geq\mu(\Omega)^2$

How to arrive at the answer $x_k= a^{-\frac{1}{p}}$?

Metric-space complete?

$\left \| \left \| f \right \|_{L^{p}} \right \|_{L^{q}} \leq \left \| \left \| f \right \|_{L^{q}} \right \|_{L^{p}} $ for $0<p\leq q$

Pointwise boundedness implies function included in $L^\infty$?

Conditions to ensure nice integrability of supremum of difference on neighborhood

$L^2(\mathbb{R})$ sequence such that $\sum_{n=1}^{\infty}\int_{\mathbb{R}}f_n(x)g(x)d\mu(x)=0$

Suppose $\mu$ is a finite measure on the Borel sets of $R$ such that $f(x) = \int_R f(x + t) \mu(dt)$ a.e., show $\mu(\{0\}) = 1$.

Does $(\ell^{1}(\mathbb Z), \cdot)$ have a bounded approximate identity?

Convergence in $L^2$ on $C([0,1])$ implies convergence in $L^1$.

Integrability of Riesz potential

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