Question

Does pointwise convergence to a continuous function on a closed interval imply uniform convergence?

score 4.2k · Answer 1 · 2018-07-13 16:42:47

4.2k

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Does pointwise convergence to a continuous function on a closed interval imply uniform convergence?

Published on 13 Jul 2018 - 16:42

score 92 · Answer 2 · 2018-07-14 11:45:37

92

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Prove that $\lim \limits_{n\to \infty}\int_{n}^{\infty} f_{n}(x)dx\neq \int_{n}^{\infty} f(x)dx $

Published on 14 Jul 2018 - 11:45

score 425 · Answer 3 · 2018-07-19 12:08:35

425

Views

Pointwise convergence to $\exp(-x^2)$ implies uniform convergence in set of functions of compact support

Published on 19 Jul 2018 - 12:08

score 201 · Answer 4 · 2026-02-22 23:26:27

201

Views

Does an integral inequality imply a pointwise inequality?

Published on 22 Feb 2026 - 23:26

score 152 · Answer 5 · 2018-08-13 22:53:12

152

Views

Convergence in measure of a bounded sequence in $L^{2}[0, 1]$ implies weak convergence

Published on 13 Aug 2018 - 22:53

score 46 · Answer 6 · 2018-08-17 04:37:07

46

Views

Convergence of $h_{n}(x) = x^{ 1 +\frac{1}{2n-1} }$ defined on [-1,1]

Published on 17 Aug 2018 - 4:37

score 58 · Answer 7 · 2018-08-20 17:07:08

58

Views

Why do we need to use dominated convergence theorem?

Published on 20 Aug 2018 - 17:07

score 445 · Answer 8 · 2018-08-20 20:21:08

445

Views

Pointwise convergence of sequence $(f_n)_n$ of functions to $f$ and changing limits

Published on 20 Aug 2018 - 20:21

score 50 · Answer 9 · 2018-08-20 23:28:55

50

Views

Difference between convergent in Measure and convergent a.e.

Published on 20 Aug 2018 - 23:28

score 53 · Answer 10 · 2018-09-02 07:09:22

53

Views

Interval of convergence, pointwise and absolute

Published on 02 Sep 2018 - 7:09

score 2.8k · Answer 11 · 2018-09-14 13:24:27

2.8k

Views

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

Published on 14 Sep 2018 - 13:24

score 33 · Answer 12 · 2018-09-17 11:29:27

33

Views

Converge in norm and converge point wise are not equivalent.

Published on 17 Sep 2018 - 11:29

score 194 · Answer 13 · 2018-09-18 12:39:19

194

Views

What exactly is the contradiction in proving that $h_n(x)$ does not converge uniformly on any bounded interval?

Published on 18 Sep 2018 - 12:39

score 264 · Answer 14 · 2018-09-22 12:00:45

264

Views

Pointwise convergence and convergence of integral

Published on 22 Sep 2018 - 12:00

score 38 · Answer 15 · 2018-09-26 11:01:23

38

Views

Showing $\sqrt[4]{n}(Y_n/\sqrt{n} - 1) \xrightarrow{D} N(0,1)$ using characteristic functions, for $Y_n \sim Bin(n, 1/\sqrt n)$

Published on 26 Sep 2018 - 11:01

List Question

Does pointwise convergence to a continuous function on a closed interval imply uniform convergence?

Prove that $\lim \limits_{n\to \infty}\int_{n}^{\infty} f_{n}(x)dx\neq \int_{n}^{\infty} f(x)dx $

Pointwise convergence to $\exp(-x^2)$ implies uniform convergence in set of functions of compact support

Does an integral inequality imply a pointwise inequality?

Convergence in measure of a bounded sequence in $L^{2}[0, 1]$ implies weak convergence

Convergence of $h_{n}(x) = x^{ 1 +\frac{1}{2n-1} }$ defined on [-1,1]

Why do we need to use dominated convergence theorem?

Pointwise convergence of sequence $(f_n)_n$ of functions to $f$ and changing limits

Difference between convergent in Measure and convergent a.e.

Interval of convergence, pointwise and absolute

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

Converge in norm and converge point wise are not equivalent.

What exactly is the contradiction in proving that $h_n(x)$ does not converge uniformly on any bounded interval?

Pointwise convergence and convergence of integral

Showing $\sqrt[4]{n}(Y_n/\sqrt{n} - 1) \xrightarrow{D} N(0,1)$ using characteristic functions, for $Y_n \sim Bin(n, 1/\sqrt n)$

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