Question

Under what circumstances convergence almost surely can be concluded from ucp convergence?

score 133 · Answer 1 · 2026-04-11 20:12:44

133

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Under what circumstances convergence almost surely can be concluded from ucp convergence?

Published on 11 Apr 2026 - 20:12

score 70 · Answer 2 · 2026-04-17 02:29:08

70

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Let $\{f_n\}$ be sequence of continously diff. func. converging uniformly to $f$ such that $f_n'(1)=0$ for all $n$. Is it necessary that $f'(1)=0$?

Published on 17 Apr 2026 - 2:29

score 111 · Answer 3 · 2026-04-15 16:22:38

111

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Find $F=\lim_{n\to \infty}F_n$ where $ F_n(x)=\sum_{k=1}^{n} \frac{x}{n}f(\frac{kx}{n}) $ and $f: [0,1]\to \mathbb R$ is continuous

Published on 15 Apr 2026 - 16:22

score 259 · Answer 4 · 2026-04-16 20:04:39

259

Views

$ f_{n}(x)=\sqrt{nx}\arctan\frac{1}{nx}$. Is the convergence uniform for $x\gt0$?

Published on 16 Apr 2026 - 20:04

score 173 · Answer 5 · 2026-04-14 03:55:27

173

Views

uniform convergence of series at endpoints

Published on 14 Apr 2026 - 3:55

score 334 · Answer 6 · 2026-04-16 09:39:01

334

Views

Show the series converges uniformly $\sum_{n =1}^\infty \frac{n^2x^2}{n^4+x^4} $

Published on 16 Apr 2026 - 9:39

score 176 · Answer 7 · 2026-04-16 20:36:09

176

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$\lim_{n \to \infty}n \left[ \int_0^n \frac{g(t)f(\frac{t}{n})}{n}dt\right]$

Published on 16 Apr 2026 - 20:36

score 2.1k · Answer 8 · 2026-04-11 23:57:36

2.1k

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Counter example: strong convergence does not imply convergence in operator norm

Published on 11 Apr 2026 - 23:57

score 119 · Answer 9 · 2026-04-15 23:54:13

119

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Lipschitz constant. How to show this inequality?

Published on 15 Apr 2026 - 23:54

score 780 · Answer 10 · 2026-04-13 23:20:29

780

Views

Uniform convergence for uniformly bounded, monotonic sequence of continuous functions over a compact set

Published on 13 Apr 2026 - 23:20

score 70 · Answer 11 · 2026-04-15 16:14:39

70

Views

$f(K) \cup \left(\bigcup_{i=1}^\infty f_i(K)\right)$ is compact

Published on 15 Apr 2026 - 16:14

score 76 · Answer 12 · 2026-04-16 08:18:34

76

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Example of a sequence $(f_n)_n$, such that $(f_ n')_n$ converges uniformly, but $(f_n)_n$ doesn't converge in any point.

Published on 16 Apr 2026 - 8:18

score 96 · Answer 13 · 2026-04-14 23:44:15

96

Views

Uniform convergence of product of cosines

Published on 14 Apr 2026 - 23:44

score 771 · Answer 14 · 2026-04-17 05:59:42

771

Views

If $f_n \to f$ uniformly and $g_n\to g$ uniformly, then $f_n\circ g_n \to f\circ g$ uniformly?

Published on 17 Apr 2026 - 5:59

score 965 · Answer 15 · 2026-04-14 18:47:44

965

Views

Why isn't $nxe^{-nx}$ uniformly convergent for $x \geq 0$?

Published on 14 Apr 2026 - 18:47

List Question

Under what circumstances convergence almost surely can be concluded from ucp convergence?

Let $\{f_n\}$ be sequence of continously diff. func. converging uniformly to $f$ such that $f_n'(1)=0$ for all $n$. Is it necessary that $f'(1)=0$?

Find $F=\lim_{n\to \infty}F_n$ where $ F_n(x)=\sum_{k=1}^{n} \frac{x}{n}f(\frac{kx}{n}) $ and $f: [0,1]\to \mathbb R$ is continuous

$ f_{n}(x)=\sqrt{nx}\arctan\frac{1}{nx}$. Is the convergence uniform for $x\gt0$?

uniform convergence of series at endpoints

Show the series converges uniformly $\sum_{n =1}^\infty \frac{n^2x^2}{n^4+x^4} $

$\lim_{n \to \infty}n \left[ \int_0^n \frac{g(t)f(\frac{t}{n})}{n}dt\right]$

Counter example: strong convergence does not imply convergence in operator norm

Lipschitz constant. How to show this inequality?

Uniform convergence for uniformly bounded, monotonic sequence of continuous functions over a compact set

$f(K) \cup \left(\bigcup_{i=1}^\infty f_i(K)\right)$ is compact

Example of a sequence $(f_n)_n$, such that $(f_ n')_n$ converges uniformly, but $(f_n)_n$ doesn't converge in any point.

Uniform convergence of product of cosines

If $f_n \to f$ uniformly and $g_n\to g$ uniformly, then $f_n\circ g_n \to f\circ g$ uniformly?

Why isn't $nxe^{-nx}$ uniformly convergent for $x \geq 0$?

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