Question

$L^2$ boundness of derivatives of a uniformly convergent sequence?

score 43 · Answer 1 · 2019-11-10 20:04:14

43

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$L^2$ boundness of derivatives of a uniformly convergent sequence?

Published on 10 Nov 2019 - 20:04

score 62 · Answer 2 · 2019-11-10 21:37:13

62

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Does $f_n (x) = \frac{x^n}{1+x^n}$ converge uniformly on $x \in [0,1]$?

Published on 10 Nov 2019 - 21:37

score 58 · Answer 3 · 2026-02-23 21:33:07

58

Views

prove pointwise convergence and uniform convergence

Published on 23 Feb 2026 - 21:33

score 345 · Answer 4 · 2019-11-13 05:11:22

345

Views

$\{f_n\}_{n=1}^{\infty}$ (each bounded) converges uniformly to $f$ then $\{f_n\}_{n=1}^{\infty}$ is uniformly bounded

Published on 13 Nov 2019 - 5:11

score 43 · Answer 5 · 2026-02-23 21:30:51

43

Views

Pointwise convergent but not uniform convergent function example clarification

Published on 23 Feb 2026 - 21:30

score 60 · Answer 6 · 2019-11-13 15:23:58

60

Views

Does $y_n=\frac{nt}{1+nt}$ converge in the space $(C[0,1], d_\infty)$?

Published on 13 Nov 2019 - 15:23

score 78 · Answer 7 · 2019-11-13 18:16:02

78

Views

Testing uniform convergence of a sequence of functions involving sums of arctan

Published on 13 Nov 2019 - 18:16

score 46 · Answer 8 · 2019-11-14 01:01:33

46

Views

Is the limit of the slopes of lines equal to the slope of the limit?

Published on 14 Nov 2019 - 1:01

score 70 · Answer 9 · 2026-02-24 02:14:54

70

Views

Uniform convergence of $f_n(x) = \frac{nx}{1+ n^2 x^2}$ - Where is the flaw?

Published on 24 Feb 2026 - 2:14

score 42 · Answer 10 · 2026-02-24 02:13:52

42

Views

Please verify my argument for $f_n(x)=x^n$ not uniformly convergent on $(0,1)$

Published on 24 Feb 2026 - 2:13

score 130 · Answer 11 · 2019-11-14 18:55:21

130

Views

Condition for $\int_{a}^{b}f_n(x)dx\rightarrow\int_{a}^{b}f(x)dx$

Published on 14 Nov 2019 - 18:55

score 59 · Answer 12 · 2019-11-14 19:25:43

59

Views

Uniform convergence preserves continuity - limit interchange argument

Published on 14 Nov 2019 - 19:25

score 79 · Answer 13 · 2019-11-15 22:36:34

79

Views

What is an example of a compact convergent series of holomorphic functions, which is not uniformly convergent?

Published on 15 Nov 2019 - 22:36

score 53 · Answer 14 · 2026-04-03 17:13:33

53

Views

Uniform Convergence on Compact Hausdorff Space

Published on 03 Apr 2026 - 17:13

score 103 · Answer 15 · 2019-11-16 13:18:10

103

Views

Pointwise convergence implying uniform convergence given value of integrals

Published on 16 Nov 2019 - 13:18

List Question

$L^2$ boundness of derivatives of a uniformly convergent sequence?

Does $f_n (x) = \frac{x^n}{1+x^n}$ converge uniformly on $x \in [0,1]$?

prove pointwise convergence and uniform convergence

$\{f_n\}_{n=1}^{\infty}$ (each bounded) converges uniformly to $f$ then $\{f_n\}_{n=1}^{\infty}$ is uniformly bounded

Pointwise convergent but not uniform convergent function example clarification

Does $y_n=\frac{nt}{1+nt}$ converge in the space $(C[0,1], d_\infty)$?

Testing uniform convergence of a sequence of functions involving sums of arctan

Is the limit of the slopes of lines equal to the slope of the limit?

Uniform convergence of $f_n(x) = \frac{nx}{1+ n^2 x^2}$ - Where is the flaw?

Please verify my argument for $f_n(x)=x^n$ not uniformly convergent on $(0,1)$

Condition for $\int_{a}^{b}f_n(x)dx\rightarrow\int_{a}^{b}f(x)dx$

Uniform convergence preserves continuity - limit interchange argument

What is an example of a compact convergent series of holomorphic functions, which is not uniformly convergent?

Uniform Convergence on Compact Hausdorff Space

Pointwise convergence implying uniform convergence given value of integrals

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