Question

Uniform convergence of sequence of functions that converges pointwise to an unbounded function

score 519 · Answer 1 · 2022-04-14 03:45:20

519

Views

Uniform convergence of sequence of functions that converges pointwise to an unbounded function

Published on 14 Apr 2022 - 3:45

score 41 · Answer 2 · 2022-04-17 01:46:08

41

Views

$W^{1,\infty}$ convergence vs Lipschitz convergence

Published on 17 Apr 2022 - 1:46

score 96 · Answer 3 · 2022-04-19 21:29:40

96

Views

Why does the following sequence of functions converge pointwise?

Published on 19 Apr 2022 - 21:29

score 173 · Answer 4 · 2022-04-28 05:41:37

173

Views

A sort of converse of Banach-Steinhaus theorem.

Published on 28 Apr 2022 - 5:41

score 115 · Answer 5 · 2022-04-28 15:08:31

115

Views

uniform convergence of $\sum_{n=1}^\infty (1-e^{-\frac xn})\sin(nx)$

Published on 28 Apr 2022 - 15:08

score 73 · Answer 6 · 2022-05-01 18:20:40

73

Views

A topology product problem with sequence of continuous and unbounded functions

Published on 01 May 2022 - 18:20

score 115 · Answer 7 · 2022-05-04 20:26:25

115

Views

Show that sequence must be in $ℓ^\infty$

Published on 04 May 2022 - 20:26

score 960 · Answer 8 · 2022-05-09 02:10:14

960

Views

Let $f_n(x) = (x-\frac{1}{n})^2$ for $x\in[0,1]$.

Published on 09 May 2022 - 2:10

score 278 · Answer 9 · 2022-05-11 22:02:06

278

Views

If {fn} converges pointwise to {f} and each {fn} is bounded in a closed interval [a,b], is {f} also bounded in [a,b]?

Published on 11 May 2022 - 22:02

score 50 · Answer 10 · 2022-05-18 13:41:42

50

Views

$\lim\limits_{n\to\infty}\int_0^2 \frac{nx^{n-1}e^{-x^n}}{1+x}dx=1-\lim\limits_{n\to\infty}\int_0^2\frac{e^{-x^n}}{(1+x)^2}dx$

Published on 18 May 2022 - 13:41

score 164 · Answer 11 · 2022-05-19 21:02:52

164

Views

problem on $L^2$ (pointwise) convergence and Carleson's Theorem

Published on 19 May 2022 - 21:02

score 159 · Answer 12 · 2022-05-22 11:19:38

159

Views

Lebesgue Dominated Convergence Theorem, $\sin(\frac{x}{n})$ example

Published on 22 May 2022 - 11:19

score 52 · Answer 13 · 2022-05-25 16:18:10

52

Views

Equality of infimal integral over family of functions, with and without pointwise closure

Published on 25 May 2022 - 16:18

score 71 · Answer 14 · 2022-05-28 07:35:01

71

Views

Convergence of integrals without the dominated convergence theorem

Published on 28 May 2022 - 7:35

score 353 · Answer 15 · 2022-05-31 16:20:39

353

Views

Does uniform integrability imply almost sure convergence of a subsequence?

Published on 31 May 2022 - 16:20

List Question

Uniform convergence of sequence of functions that converges pointwise to an unbounded function

$W^{1,\infty}$ convergence vs Lipschitz convergence

Why does the following sequence of functions converge pointwise?

A sort of converse of Banach-Steinhaus theorem.

uniform convergence of $\sum_{n=1}^\infty (1-e^{-\frac xn})\sin(nx)$

A topology product problem with sequence of continuous and unbounded functions

Show that sequence must be in $ℓ^\infty$

Let $f_n(x) = (x-\frac{1}{n})^2$ for $x\in[0,1]$.

If {fn} converges pointwise to {f} and each {fn} is bounded in a closed interval [a,b], is {f} also bounded in [a,b]?

$\lim\limits_{n\to\infty}\int_0^2 \frac{nx^{n-1}e^{-x^n}}{1+x}dx=1-\lim\limits_{n\to\infty}\int_0^2\frac{e^{-x^n}}{(1+x)^2}dx$

problem on $L^2$ (pointwise) convergence and Carleson's Theorem

Lebesgue Dominated Convergence Theorem, $\sin(\frac{x}{n})$ example

Equality of infimal integral over family of functions, with and without pointwise closure

Convergence of integrals without the dominated convergence theorem

Does uniform integrability imply almost sure convergence of a subsequence?

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