Question

If $f$ is a homeomorphism

score 142 · Answer 1 · 2017-03-02 13:35:14

142

Views

If $f$ is a homeomorphism

Published on 02 Mar 2017 - 13:35

score 50 · Answer 2 · 2017-03-02 19:11:09

50

Views

A problem of uniform convergence of a sequence of functions

Published on 02 Mar 2017 - 19:11

score 132 · Answer 3 · 2017-03-02 22:03:15

132

Views

What is wrong with this proof that $\lim_{n \to \infty} \int_0^\frac{\pi}{2} f(x)\sin(nx)dx=0$

Published on 02 Mar 2017 - 22:03

score 187 · Answer 4 · 2017-03-03 23:21:59

187

Views

Uniform convergence and continuity proof

Published on 03 Mar 2017 - 23:21

score 1.2k · Answer 5 · 2017-03-04 15:37:29

1.2k

Views

Uniform convergence of $\frac{x}{1+n^2x^2}$

Published on 04 Mar 2017 - 15:37

score 602 · Answer 6 · 2017-03-06 16:19:00

602

Views

Is this product/quotient of two uniformly convergent functions uniformly convergent?

Published on 06 Mar 2017 - 16:19

score 445 · Answer 7 · 2017-03-07 16:15:21

445

Views

To show $\sum_{n=1}^{\infty}\frac{x}{n^{\alpha}(1+nx^{2})}$ converges uniformly

Published on 07 Mar 2017 - 16:15

score 149 · Answer 8 · 2026-04-01 06:54:51

149

Views

Convergence of Compactly Supported $C^{\infty}$ Functions

Published on 01 Apr 2026 - 6:54

score 721 · Answer 9 · 2017-03-09 07:14:36

721

Views

Prove that $\sum_{n=1}^{\infty} (\frac{\ln x}{x})^n$ converge uniformly

Published on 09 Mar 2017 - 7:14

score 74 · Answer 10 · 2017-03-09 12:08:08

74

Views

How can I show that this sequence of derivatives converges uniformly on [-R,R] for $R>0$

Published on 09 Mar 2017 - 12:08

score 60 · Answer 11 · 2017-03-10 04:33:52

60

Views

Is $\sum_{n=1}^{\infty} \frac{x}{n^{1+a}}$ converge pointwisely on $R$?

Published on 10 Mar 2017 - 4:33

score 916 · Answer 12 · 2026-04-01 02:02:51

916

Views

Let $g\in C[a,b]$, $\{f_n\}$ is a sequence of continuous functions, and $f_n\to f$ uniformly. Prove $\lim_{n\to\infty}\int_a^bf_ng = \int_a^bfg$

Published on 01 Apr 2026 - 2:02

score 114 · Answer 13 · 2017-03-11 20:10:25

114

Views

Prove that $f_n$ = $\frac{x}{1+n^2x^2}$ uniformly converges.

Published on 11 Mar 2017 - 20:10

score 1.3k · Answer 14 · 2017-03-12 01:29:30

1.3k

Views

a counter example to the fact that bounded convergence theorem holds if we drop the assumption that sequence is uniformly bounded.

Published on 12 Mar 2017 - 1:29

score 443 · Answer 15 · 2017-03-12 19:43:29

443

Views

Egorov's Theorem: Royden / Fitzpatrick

Published on 12 Mar 2017 - 19:43

List Question

If $f$ is a homeomorphism

A problem of uniform convergence of a sequence of functions

What is wrong with this proof that $\lim_{n \to \infty} \int_0^\frac{\pi}{2} f(x)\sin(nx)dx=0$

Uniform convergence and continuity proof

Uniform convergence of $\frac{x}{1+n^2x^2}$

Is this product/quotient of two uniformly convergent functions uniformly convergent?

To show $\sum_{n=1}^{\infty}\frac{x}{n^{\alpha}(1+nx^{2})}$ converges uniformly

Convergence of Compactly Supported $C^{\infty}$ Functions

Prove that $\sum_{n=1}^{\infty} (\frac{\ln x}{x})^n$ converge uniformly

How can I show that this sequence of derivatives converges uniformly on [-R,R] for $R>0$

Is $\sum_{n=1}^{\infty} \frac{x}{n^{1+a}}$ converge pointwisely on $R$?

Let $g\in C[a,b]$, $\{f_n\}$ is a sequence of continuous functions, and $f_n\to f$ uniformly. Prove $\lim_{n\to\infty}\int_a^bf_ng = \int_a^bfg$

Prove that $f_n$ = $\frac{x}{1+n^2x^2}$ uniformly converges.

a counter example to the fact that bounded convergence theorem holds if we drop the assumption that sequence is uniformly bounded.

Egorov's Theorem: Royden / Fitzpatrick

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