Question

Prove that if $(f_n)_{n \geq 1} \to f$ uniformly then $f_n \to f \in B(X)$

score 63 · Answer 1 · 2015-06-08 22:06:43

63

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Prove that if $(f_n)_{n \geq 1} \to f$ uniformly then $f_n \to f \in B(X)$

Published on 08 Jun 2015 - 22:06

score 1.1k · Answer 2 · 2026-04-11 15:32:47

1.1k

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Is limit function of continuous even functions always continuous?

Published on 11 Apr 2026 - 15:32

score 245 · Answer 3 · 2015-06-09 09:21:13

245

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Prove that $f_n(x)$ converges uniformly on $[1,\infty)$ but not on $(0,1)$.

Published on 09 Jun 2015 - 9:21

score 306 · Answer 4 · 2026-04-01 05:12:46

306

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If $(f_n)_{n\geq 1} \to f$ uniformly and $(g_n)_{n\geq 1} \to g$ uniformly then $(f_n \circ g_n)_{n\geq 1} \to f\circ g$ uniformly

Published on 01 Apr 2026 - 5:12

score 360 · Answer 5 · 2026-03-26 01:29:20

360

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Have you ever seen this result about pointwise/uniform convergence of a net of continuous functions?

Published on 26 Mar 2026 - 1:29

score 362 · Answer 6 · 2026-04-12 03:12:48

362

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Alternate proof for Arzela-Ascoli

Published on 12 Apr 2026 - 3:12

score 312 · Answer 7 · 2026-04-08 17:45:21

312

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Tricky problem dealing with limits of multiple integration,

Published on 08 Apr 2026 - 17:45

score 1.5k · Answer 8 · 2026-04-12 06:38:19

1.5k

Views

Uniform convergence in distribution

Published on 12 Apr 2026 - 6:38

score 108 · Answer 9 · 2026-04-12 08:28:18

108

Views

Uniform convergence for sequence

Published on 12 Apr 2026 - 8:28

score 109 · Answer 10 · 2015-06-15 14:45:48

109

Views

Prove $f_n(x)$ converges pointwise to some $f(x)$ but the convergence is not uniform

Published on 15 Jun 2015 - 14:45

score 1.1k · Answer 11 · 2026-04-11 22:04:22

1.1k

Views

Convergence in distribution and weak convergence implies convergence of expectations

Published on 11 Apr 2026 - 22:04

score 116 · Answer 12 · 2026-04-11 02:16:00

116

Views

Uniform convergence method?

Published on 11 Apr 2026 - 2:16

score 92 · Answer 13 · 2026-04-09 08:11:36

92

Views

Help with convergence of series of functions

Published on 09 Apr 2026 - 8:11

score 806 · Answer 14 · 2015-06-20 10:41:03

806

Views

Does the Taylor series of $\ln (1-x)$ converge uniformly on $[0, 1)$?

Published on 20 Jun 2015 - 10:41

score 922 · Answer 15 · 2015-06-20 15:21:12

922

Views

If $f_n \to f$ uniformly and $f$ is continuous, does that imply $f_n$ is continuous?

Published on 20 Jun 2015 - 15:21

List Question

Prove that if $(f_n)_{n \geq 1} \to f$ uniformly then $f_n \to f \in B(X)$

Is limit function of continuous even functions always continuous?

Prove that $f_n(x)$ converges uniformly on $[1,\infty)$ but not on $(0,1)$.

If $(f_n)_{n\geq 1} \to f$ uniformly and $(g_n)_{n\geq 1} \to g$ uniformly then $(f_n \circ g_n)_{n\geq 1} \to f\circ g$ uniformly

Have you ever seen this result about pointwise/uniform convergence of a net of continuous functions?

Alternate proof for Arzela-Ascoli

Tricky problem dealing with limits of multiple integration,

Uniform convergence in distribution

Uniform convergence for sequence

Prove $f_n(x)$ converges pointwise to some $f(x)$ but the convergence is not uniform

Convergence in distribution and weak convergence implies convergence of expectations

Uniform convergence method?

Help with convergence of series of functions

Does the Taylor series of $\ln (1-x)$ converge uniformly on $[0, 1)$?

If $f_n \to f$ uniformly and $f$ is continuous, does that imply $f_n$ is continuous?

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