Question

If a series converges uniformly on $[a+\varepsilon,b) $ for all $\varepsilon>0$ and pointwise on $[a,b)$, is then the convergence uniform on $[a,b) $?

score 100 · Answer 1 · 2017-12-07 11:49:05

100

Views

If a series converges uniformly on $[a+\varepsilon,b) $ for all $\varepsilon>0$ and pointwise on $[a,b)$, is then the convergence uniform on $[a,b) $?

Published on 07 Dec 2017 - 11:49

score 365 · Answer 2 · 2017-12-07 20:39:16

365

Views

Pointwise Limit of a Sequence of Measurable Functions

Published on 07 Dec 2017 - 20:39

score 78 · Answer 3 · 2017-12-13 11:30:50

78

Views

If a sequence of functions tends to infinity pointwise, does it also tend to infinity uniformly?

Published on 13 Dec 2017 - 11:30

score 239 · Answer 4 · 2017-12-26 10:23:06

239

Views

Examine the uniform convergence of the series of functions $f_n: \mathbb{R} \to \mathbb{R}: x \mapsto \frac{(-1)^n}{n}$

Published on 26 Dec 2017 - 10:23

score 414 · Answer 5 · 2017-12-26 11:08:54

414

Views

Examine uniform convergence of the series of functions with $f_n: [1,2] \to \mathbb{R}: x \mapsto xe^{-nx}$

Published on 26 Dec 2017 - 11:08

score 1.3k · Answer 6 · 2017-12-26 22:27:21

1.3k

Views

Show that a series of functions converges (uniformly)

Published on 26 Dec 2017 - 22:27

score 184 · Answer 7 · 2018-01-01 19:03:59

184

Views

Criteria for smoothness of the pointwise limit of a sequence of functions

Published on 01 Jan 2018 - 19:03

score 139 · Answer 8 · 2018-01-02 10:05:46

139

Views

Show convergence of the series of functions $\sum_{n=1}^\infty \frac{x}{n^\alpha (1+nx^2)}$

Published on 02 Jan 2018 - 10:05

score 118 · Answer 9 · 2018-01-03 12:38:09

118

Views

Prove that $\sum_{n=1}^\infty f_n$ converges uniformly on $\mathbb{R}$ where $f_n$ is defined piecewise.

Published on 03 Jan 2018 - 12:38

score 442 · Answer 10 · 2018-01-03 16:35:42

442

Views

Pointwise & Absolute convergence- What are ε and ?

Published on 03 Jan 2018 - 16:35

score 561 · Answer 11 · 2018-01-04 19:42:28

561

Views

pointwise convergence of a piecewise function with intervals dependent on n

Published on 04 Jan 2018 - 19:42

score 327 · Answer 12 · 2018-01-08 19:37:12

327

Views

Pointwise and uniform convergence of $\sum_{n=1}^{+\infty}\big({\frac{x}{1+x^n}}\big)^n$

Published on 08 Jan 2018 - 19:37

score 370 · Answer 13 · 2018-01-09 15:09:49

370

Views

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

Published on 09 Jan 2018 - 15:09

score 394 · Answer 14 · 2018-01-12 06:41:55

394

Views

Uniform convergence of $n\sin\sqrt{4\pi^2n^2+x^2}$ on $[0,a]$ and $\mathbb{R}.$

Published on 12 Jan 2018 - 6:41

score 2.5k · Answer 15 · 2012-02-12 20:39:03

2.5k

Views

Pointwise limit of continuous functions not Riemann integrable

Published on 12 Feb 2012 - 20:39

List Question

If a series converges uniformly on $[a+\varepsilon,b) $ for all $\varepsilon>0$ and pointwise on $[a,b)$, is then the convergence uniform on $[a,b) $?

Pointwise Limit of a Sequence of Measurable Functions

If a sequence of functions tends to infinity pointwise, does it also tend to infinity uniformly?

Examine the uniform convergence of the series of functions $f_n: \mathbb{R} \to \mathbb{R}: x \mapsto \frac{(-1)^n}{n}$

Examine uniform convergence of the series of functions with $f_n: [1,2] \to \mathbb{R}: x \mapsto xe^{-nx}$

Show that a series of functions converges (uniformly)

Criteria for smoothness of the pointwise limit of a sequence of functions

Show convergence of the series of functions $\sum_{n=1}^\infty \frac{x}{n^\alpha (1+nx^2)}$

Prove that $\sum_{n=1}^\infty f_n$ converges uniformly on $\mathbb{R}$ where $f_n$ is defined piecewise.

Pointwise & Absolute convergence- What are ε and ?

pointwise convergence of a piecewise function with intervals dependent on n

Pointwise and uniform convergence of $\sum_{n=1}^{+\infty}\big({\frac{x}{1+x^n}}\big)^n$

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

Uniform convergence of $n\sin\sqrt{4\pi^2n^2+x^2}$ on $[0,a]$ and $\mathbb{R}.$

Pointwise limit of continuous functions not Riemann integrable

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