Question

If $f(x)$ uniformly continuous implies $f_n(x):=f(x+1/n)$ uniformly convergent

score 472 · Answer 1 · 2026-03-30 07:11:35

472

Views

If $f(x)$ uniformly continuous implies $f_n(x):=f(x+1/n)$ uniformly convergent

Published on 30 Mar 2026 - 7:11

score 386 · Answer 2 · 2026-03-26 11:00:05

386

Views

Convergence of arc lengths of a sequence

Published on 26 Mar 2026 - 11:00

score 24 · Answer 3 · 2016-11-30 11:23:38

24

Views

Uniform convergence of a sequence of integrals

Published on 30 Nov 2016 - 11:23

score 51 · Answer 4 · 2026-03-30 10:39:29

51

Views

$V_2$ is complete implies set of all continuous bounded functions $f:V_1\to V_2$ complete

Published on 30 Mar 2026 - 10:39

score 80 · Answer 5 · 2016-12-02 07:56:51

80

Views

prove a set is closed in $C^0$

Published on 02 Dec 2016 - 7:56

score 382 · Answer 6 · 2026-04-02 13:25:22

382

Views

Sequence of real analytic functions $f_{n}(x):\mathbb{R} \rightarrow \mathbb{R}$ converges uniformly to absolute value function $f(x)=|x|$

Published on 02 Apr 2026 - 13:25

score 75 · Answer 7 · 2016-12-05 05:51:50

75

Views

Show that $f_{n}(x)= \frac{1}{1+x^n}$ does not converge uniformly to $f(x)$ on $[0,1]$

Published on 05 Dec 2016 - 5:51

score 311 · Answer 8 · 2016-12-05 23:03:40

311

Views

Uniform Law of Large numbers for independent but non-identical random matrices

Published on 05 Dec 2016 - 23:03

score 939 · Answer 9 · 2016-12-06 17:46:10

939

Views

Example of a series of functions that converges for Leibniz rule but is not uniformly convergent?

Published on 06 Dec 2016 - 17:46

score 989 · Answer 10 · 2016-12-06 18:53:04

989

Views

Uniform and absolute convergence of improper integral

Published on 06 Dec 2016 - 18:53

score 696 · Answer 11 · 2026-03-26 17:34:29

696

Views

Example of a series of functions that converges absolutely but does not converges uniformly?

Published on 26 Mar 2026 - 17:34

score 515 · Answer 12 · 2016-12-07 14:36:20

515

Views

Convergence of $f_n(z) = \sin(z/n)$

Published on 07 Dec 2016 - 14:36

score 178 · Answer 13 · 2016-12-09 19:07:54

178

Views

Show that $\sum_{k=0}^\infty \frac{(−1)^k}{(2k+1)!} x^{2k+1}$ converges uniformly on $[−a,a]$ for every $a>0$ , but not uniformly on R.

Published on 09 Dec 2016 - 19:07

score 455 · Answer 14 · 2016-12-10 18:21:57

455

Views

Uniform convergence for $\sum_{k=1}^{\infty} (-1)^{k}e^{-kx} $

Published on 10 Dec 2016 - 18:21

score 1.2k · Answer 15 · 2016-12-11 15:18:15

1.2k

Views

$\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.

Published on 11 Dec 2016 - 15:18

List Question

If $f(x)$ uniformly continuous implies $f_n(x):=f(x+1/n)$ uniformly convergent

Convergence of arc lengths of a sequence

Uniform convergence of a sequence of integrals

$V_2$ is complete implies set of all continuous bounded functions $f:V_1\to V_2$ complete

prove a set is closed in $C^0$

Sequence of real analytic functions $f_{n}(x):\mathbb{R} \rightarrow \mathbb{R}$ converges uniformly to absolute value function $f(x)=|x|$

Show that $f_{n}(x)= \frac{1}{1+x^n}$ does not converge uniformly to $f(x)$ on $[0,1]$

Uniform Law of Large numbers for independent but non-identical random matrices

Example of a series of functions that converges for Leibniz rule but is not uniformly convergent?

Uniform and absolute convergence of improper integral

Example of a series of functions that converges absolutely but does not converges uniformly?

Convergence of $f_n(z) = \sin(z/n)$

Show that $\sum_{k=0}^\infty \frac{(−1)^k}{(2k+1)!} x^{2k+1}$ converges uniformly on $[−a,a]$ for every $a>0$ , but not uniformly on R.

Uniform convergence for $\sum_{k=1}^{\infty} (-1)^{k}e^{-kx} $

$\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.

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