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 101 · Answer 1 · 2026-02-25 08:50:47

101

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 25 Feb 2026 - 8:50

score 367 · Answer 2 · 2026-04-13 01:58:23

367

Views

Pointwise Limit of a Sequence of Measurable Functions

Published on 13 Apr 2026 - 1:58

score 79 · Answer 3 · 2026-02-25 08:55:01

79

Views

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

Published on 25 Feb 2026 - 8:55

score 240 · Answer 4 · 2026-02-25 08:53:08

240

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 25 Feb 2026 - 8:53

score 415 · Answer 5 · 2026-02-25 08:51:27

415

Views

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

Published on 25 Feb 2026 - 8:51

score 1.3k · Answer 6 · 2026-02-25 08:50:00

1.3k

Views

Show that a series of functions converges (uniformly)

Published on 25 Feb 2026 - 8:50

score 185 · Answer 7 · 2026-02-25 08:50:05

185

Views

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

Published on 25 Feb 2026 - 8:50

score 140 · Answer 8 · 2026-02-25 08:50:46

140

Views

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

Published on 25 Feb 2026 - 8:50

score 119 · Answer 9 · 2026-02-25 08:55:18

119

Views

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

Published on 25 Feb 2026 - 8:55

score 445 · Answer 10 · 2026-04-09 22:35:30

445

Views

Pointwise & Absolute convergence- What are ε and ?

Published on 09 Apr 2026 - 22:35

score 563 · Answer 11 · 2026-04-13 09:30:09

563

Views

pointwise convergence of a piecewise function with intervals dependent on n

Published on 13 Apr 2026 - 9:30

score 328 · Answer 12 · 2026-02-25 08:50:05

328

Views

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

Published on 25 Feb 2026 - 8:50

score 371 · Answer 13 · 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 395 · Answer 14 · 2026-02-25 08:55:18

395

Views

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

Published on 25 Feb 2026 - 8:55

score 2.5k · Answer 15 · 2026-04-13 04:02:50

2.5k

Views

Pointwise limit of continuous functions not Riemann integrable

Published on 13 Apr 2026 - 4:02

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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