Question

Sequence of functions $f_n(x)=\frac{2x^2}{x^2+(1-2nx)^2}$, does it have a uniformly converging subsequence?

score 422 · Answer 1 · 2026-02-23 17:44:57

422

Views

Sequence of functions $f_n(x)=\frac{2x^2}{x^2+(1-2nx)^2}$, does it have a uniformly converging subsequence?

Published on 23 Feb 2026 - 17:44

score 88 · Answer 2 · 2017-12-26 03:41:25

88

Views

Almost Uniform Convergence - enough to move limits into integrals? (check proof)

Published on 26 Dec 2017 - 3:41

score 38 · Answer 3 · 2017-12-27 14:15:28

38

Views

What can I say for this function sequence $n-n^2x$

Published on 27 Dec 2017 - 14:15

score 125 · Answer 4 · 2018-01-02 21:12:12

125

Views

One-sided limits functions and monotony(proposition)

Published on 02 Jan 2018 - 21:12

score 371 · Answer 5 · 2026-02-25 08:55:01

371

Views

pointwise limit of sequence of Lipschitz continuous functions is Lipschitz continuous $\Rightarrow$ Lipschitz constants bounded?

Published on 25 Feb 2026 - 8:55

score 288 · Answer 6 · 2018-01-10 14:44:04

288

Views

Measure theory convergence in measure

Published on 10 Jan 2018 - 14:44

score 150 · Answer 7 · 2018-01-11 17:54:12

150

Views

How to conclude that there exists subsequence that converges for all $s\in S$?

Published on 11 Jan 2018 - 17:54

score 6.5k · Answer 8 · 2018-01-12 12:32:41

6.5k

Views

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Published on 12 Jan 2018 - 12:32

score 192 · Answer 9 · 2020-07-31 16:57:26

192

Views

Almost everywhere pointwise convergence

Published on 31 Jul 2020 - 16:57

score 121 · Answer 10 · 2020-07-31 19:59:37

121

Views

How do I show $\lim_{n \rightarrow \infty} \int_{0}^{1}f_{n}(x)dx=\int_{0}^{1}f(x)dx$.

Published on 31 Jul 2020 - 19:59

score 95 · Answer 11 · 2026-02-25 10:15:45

95

Views

Uniform continuity on different intervals

Published on 25 Feb 2026 - 10:15

score 61 · Answer 12 · 2026-02-25 10:17:05

61

Views

Convergence almost surely for a subsequence

Published on 25 Feb 2026 - 10:17

score 47 · Answer 13 · 2020-08-05 21:24:33

47

Views

Comparison of sequence of functions and function on $\mathbb{R}^2$

Published on 05 Aug 2020 - 21:24

score 700 · Answer 14 · 2020-08-07 17:00:01

700

Views

Let $\alpha>0$. Show that $\sum_{n=1}^\infty {\sin nx\over n^\alpha}$ converges for all $x\in\Bbb{R}$ and examine continuity of the limit function.

Published on 07 Aug 2020 - 17:00

score 35 · Answer 15 · 2026-02-25 10:17:04

35

Views

Is the set $M_j:=\{x\in[a,b]~|~g_i(x)<\epsilon~\forall i>j\}$ open?

Published on 25 Feb 2026 - 10:17

List Question

Sequence of functions $f_n(x)=\frac{2x^2}{x^2+(1-2nx)^2}$, does it have a uniformly converging subsequence?

Almost Uniform Convergence - enough to move limits into integrals? (check proof)

What can I say for this function sequence $n-n^2x$

One-sided limits functions and monotony(proposition)

pointwise limit of sequence of Lipschitz continuous functions is Lipschitz continuous $\Rightarrow$ Lipschitz constants bounded?

Measure theory convergence in measure

How to conclude that there exists subsequence that converges for all $s\in S$?

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Almost everywhere pointwise convergence

How do I show $\lim_{n \rightarrow \infty} \int_{0}^{1}f_{n}(x)dx=\int_{0}^{1}f(x)dx$.

Uniform continuity on different intervals

Convergence almost surely for a subsequence

Comparison of sequence of functions and function on $\mathbb{R}^2$

Let $\alpha>0$. Show that $\sum_{n=1}^\infty {\sin nx\over n^\alpha}$ converges for all $x\in\Bbb{R}$ and examine continuity of the limit function.

Is the set $M_j:=\{x\in[a,b]~|~g_i(x)<\epsilon~\forall i>j\}$ open?

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