Question

Why $L^2$ convergence, with Riemann Integral, does not imply pointwise convergence at any point?

score 196 · Answer 1 · 2018-09-29 22:04:37

196

Views

Why $L^2$ convergence, with Riemann Integral, does not imply pointwise convergence at any point?

Published on 29 Sep 2018 - 22:04

score 454 · Answer 2 · 2018-09-30 15:29:22

454

Views

Can we interchange integral and limit if the sequence of function is uniformly integrable?

Published on 30 Sep 2018 - 15:29

score 103 · Answer 3 · 2018-09-30 17:33:33

103

Views

If $f_n(s) \rightarrow f(s)$ for all s. Is it correct to say that $\lim_{n\to\infty}(\min f_n)=\min f$?

Published on 30 Sep 2018 - 17:33

score 1.3k · Answer 4 · 2018-10-02 15:24:54

1.3k

Views

Pointwise limit of continuous functions is continuous on a dense set

Published on 02 Oct 2018 - 15:24

score 49 · Answer 5 · 2018-10-06 09:09:16

49

Views

$\mu(\bigcup_{n=N}^\infty\omega:|g_n(\omega)-g(\omega)|>\varepsilon)<\varepsilon$ then $g_n\to g$ pointwise a.e.

Published on 06 Oct 2018 - 9:09

score 197 · Answer 6 · 2018-10-09 00:22:08

197

Views

If $\int f_nd\mu \to \int f d \mu <\infty$ then for all measurable $E$, $\int _E f_nd\mu \to \int _E f d\mu$

Published on 09 Oct 2018 - 0:22

score 110 · Answer 7 · 2018-10-09 15:43:19

110

Views

Prove $f(x,y)$ defined on $\mathbb{R}^2$ is Lebesgue Measurable if $f$ is continuous in each variable separately.

Published on 09 Oct 2018 - 15:43

score 171 · Answer 8 · 2018-10-10 18:20:15

171

Views

Strongly convergent subsequence $+$ point-wise convergence $\Rightarrow$ strong convergence?

Published on 10 Oct 2018 - 18:20

score 220 · Answer 9 · 2018-10-12 17:18:51

220

Views

Uniform convergence of $\sum\limits_{n=1}^∞n^{-x}(e^{\frac{x}{n^2}}-1)$

Published on 12 Oct 2018 - 17:18

score 136 · Answer 10 · 2026-02-23 06:39:31

136

Views

Convergence of the following sequence of functions.

Published on 23 Feb 2026 - 6:39

score 358 · Answer 11 · 2018-10-22 12:45:50

358

Views

Pointwise convergence of average of continuous functions

Published on 22 Oct 2018 - 12:45

score 141 · Answer 12 · 2026-02-23 06:40:31

141

Views

Pointwise and uniform convergence of a piecewise sequence of functions on the closed, punctured disk, $\overline{D}\prime(0,1)$.

Published on 23 Feb 2026 - 6:40

score 525 · Answer 13 · 2026-02-23 04:47:08

525

Views

A proof that the pointwise limits of lower semicontinuous (lsc) functions is lsc

Published on 23 Feb 2026 - 4:47

score 597 · Answer 14 · 2018-10-29 01:56:05

597

Views

$n\chi_{[0, 1/n]}$ converges pointwise

Published on 29 Oct 2018 - 1:56

score 32 · Answer 15 · 2018-11-02 13:10:11

32

Views

Convergence of complex sequence checkup

Published on 02 Nov 2018 - 13:10

List Question

Why $L^2$ convergence, with Riemann Integral, does not imply pointwise convergence at any point?

Can we interchange integral and limit if the sequence of function is uniformly integrable?

If $f_n(s) \rightarrow f(s)$ for all s. Is it correct to say that $\lim_{n\to\infty}(\min f_n)=\min f$?

Pointwise limit of continuous functions is continuous on a dense set

$\mu(\bigcup_{n=N}^\infty\omega:|g_n(\omega)-g(\omega)|>\varepsilon)<\varepsilon$ then $g_n\to g$ pointwise a.e.

If $\int f_nd\mu \to \int f d \mu <\infty$ then for all measurable $E$, $\int _E f_nd\mu \to \int _E f d\mu$

Prove $f(x,y)$ defined on $\mathbb{R}^2$ is Lebesgue Measurable if $f$ is continuous in each variable separately.

Strongly convergent subsequence $+$ point-wise convergence $\Rightarrow$ strong convergence?

Uniform convergence of $\sum\limits_{n=1}^∞n^{-x}(e^{\frac{x}{n^2}}-1)$

Convergence of the following sequence of functions.

Pointwise convergence of average of continuous functions

Pointwise and uniform convergence of a piecewise sequence of functions on the closed, punctured disk, $\overline{D}\prime(0,1)$.

A proof that the pointwise limits of lower semicontinuous (lsc) functions is lsc

$n\chi_{[0, 1/n]}$ converges pointwise

Convergence of complex sequence checkup

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