Question

Show $\|f\|_p\leq\|f\|_q\mu(X)^{\frac{1}{p}-\frac{1}{q}}$ whenever $0<p\leq q\leq \infty$ using log-convexity of $L^p$ norms.

score 51 · Answer 1 · 2026-03-29 05:44:06

51

Views

Show $\|f\|_p\leq\|f\|_q\mu(X)^{\frac{1}{p}-\frac{1}{q}}$ whenever $0<p\leq q\leq \infty$ using log-convexity of $L^p$ norms.

Published on 29 Mar 2026 - 5:44

score 94 · Answer 2 · 2026-03-24 22:17:17

94

Views

Image of unit ball under twice differentiable function

Published on 24 Mar 2026 - 22:17

score 324 · Answer 3 · 2026-04-09 00:33:36

324

Views

Relative volume of $\delta$-fattening (neighborhood) of a compact set

Published on 09 Apr 2026 - 0:33

score 1.6k · Answer 4 · 2026-04-10 22:10:38

1.6k

Views

Looking for a "soft" book on second semester real analysis?

Published on 10 Apr 2026 - 22:10

score 46 · Answer 5 · 2026-04-11 00:04:57

46

Views

A question about a property of independent random variables

Published on 11 Apr 2026 - 0:04

score 453 · Answer 6 · 2026-04-10 19:39:08

453

Views

Computing limit of sequence of sets defined on indicator function

Published on 10 Apr 2026 - 19:39

score 121 · Answer 7 · 2026-03-24 22:16:06

121

Views

Show that $\lim\limits_{n\to \infty}\sum\limits_{k=-n^2}^{n^2}\left|\int_{k/n}^{(k+1)/n}f(x)\,dx\right| = \int_{-\infty}^\infty |f(x)|\, dx$

Published on 24 Mar 2026 - 22:16

score 254 · Answer 8 · 2026-04-09 10:03:56

254

Views

Proof that if $f_n\to f$ a.e., $g_n \to g$ a.e. and $g_n = f_n$ a.e. implies $f=g$ a.e.

Published on 09 Apr 2026 - 10:03

score 52 · Answer 9 · 2026-04-10 19:39:03

52

Views

Can I refer to the interval $[0,1]$ as an uncountable union of singletones?

Published on 10 Apr 2026 - 19:39

score 233 · Answer 10 · 2026-04-09 06:07:49

233

Views

double integral of f zero over subsets of $[0,1]^2$ implies $f=0$ almost everywhere

Published on 09 Apr 2026 - 6:07

score 40 · Answer 11 · 2026-04-01 09:56:20

40

Views

Given $\lim_{n\to \infty}\int_A(f_{n+1}-f_n)^2d\mu=0$ ,$ \int_Xf_n^2d\mu \le k $, is {$f_n $} uniformly integrable on $A$?

Published on 01 Apr 2026 - 9:56

score 157 · Answer 12 · 2026-04-10 01:14:30

157

Views

If a function preserves integrability, must it have linear growth?

Published on 10 Apr 2026 - 1:14

score 707 · Answer 13 · 2026-04-08 23:42:46

707

Views

Poincaré's Recurrence Theorem

Published on 08 Apr 2026 - 23:42

score 978 · Answer 14 · 2018-01-28 20:20:57

978

Views

Show continuously differentiable image of Jordan measurable set is Jordan measurable

Published on 28 Jan 2018 - 20:20

score 1.3k · Answer 15 · 2026-04-10 21:17:53

1.3k

Views

What is an example of a pi-system that is not a sigma algebra?

Published on 10 Apr 2026 - 21:17

List Question

Show $\|f\|_p\leq\|f\|_q\mu(X)^{\frac{1}{p}-\frac{1}{q}}$ whenever $0<p\leq q\leq \infty$ using log-convexity of $L^p$ norms.

Image of unit ball under twice differentiable function

Relative volume of $\delta$-fattening (neighborhood) of a compact set

Looking for a "soft" book on second semester real analysis?

A question about a property of independent random variables

Computing limit of sequence of sets defined on indicator function

Show that $\lim\limits_{n\to \infty}\sum\limits_{k=-n^2}^{n^2}\left|\int_{k/n}^{(k+1)/n}f(x)\,dx\right| = \int_{-\infty}^\infty |f(x)|\, dx$

Proof that if $f_n\to f$ a.e., $g_n \to g$ a.e. and $g_n = f_n$ a.e. implies $f=g$ a.e.

Can I refer to the interval $[0,1]$ as an uncountable union of singletones?

double integral of f zero over subsets of $[0,1]^2$ implies $f=0$ almost everywhere

Given $\lim_{n\to \infty}\int_A(f_{n+1}-f_n)^2d\mu=0$ ,$ \int_Xf_n^2d\mu \le k $, is {$f_n $} uniformly integrable on $A$?

If a function preserves integrability, must it have linear growth?

Poincaré's Recurrence Theorem

Show continuously differentiable image of Jordan measurable set is Jordan measurable

What is an example of a pi-system that is not a sigma algebra?

Trending Questions

Popular # Hahtags

Popular Questions