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uniform convergence of functions over $\mathbb{R}^n$ implies integral convergence of functions with product

score 190 · Answer 1 · 2026-04-16 15:08:19

190

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uniform convergence of functions over $\mathbb{R}^n$ implies integral convergence of functions with product

Published on 16 Apr 2026 - 15:08

score 1.7k · Answer 2 · 2026-04-12 18:36:45

1.7k

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Pointwise convergence to infinity implies uniformly convergence?

Published on 12 Apr 2026 - 18:36

score 330 · Answer 3 · 2026-04-15 18:53:48

330

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Suppose $f_n\rightarrow f$ pointwise. Show that if each $f_n$ is continuous then $f$ is also continuous.

Published on 15 Apr 2026 - 18:53

score 24 · Answer 4 · 2026-04-15 02:54:09

24

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Uniform Convergence of Sequences

Published on 15 Apr 2026 - 2:54

score 228 · Answer 5 · 2026-03-30 07:09:03

228

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Help for example 19.7 in van der Vaart: show that a parametric class of functions with Lipschitz condition is Donsker

Published on 30 Mar 2026 - 7:09

score 593 · Answer 6 · 2026-04-15 20:00:57

593

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

Published on 15 Apr 2026 - 20:00

score 131 · Answer 7 · 2026-04-15 16:05:39

131

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Is the convergence to the closure pointwise or uniform?

Published on 15 Apr 2026 - 16:05

score 155 · Answer 8 · 2026-04-15 21:11:25

155

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Uniform and absolute convergence of infinite trigonometric product

Published on 15 Apr 2026 - 21:11

score 131 · Answer 9 · 2026-04-12 07:18:35

131

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Simple questions about infinite products

Published on 12 Apr 2026 - 7:18

score 1.6k · Answer 10 · 2026-04-02 01:26:11

1.6k

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If a sequence $(f_n)$ do not converge uniformly, then no subsequence of $(f_n)$ converge uniformly

Published on 02 Apr 2026 - 1:26

score 70 · Answer 11 · 2026-04-10 12:38:58

70

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Non zero continuous path $[0,1]\to \mathbb C$ has continuous logarithm

Published on 10 Apr 2026 - 12:38

score 81 · Answer 12 · 2026-04-13 23:20:33

81

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Uniform convergence of $f_n(x)=nx^{n-1}$ on $[0,1)$.

Published on 13 Apr 2026 - 23:20

score 132 · Answer 13 · 2026-04-15 16:36:21

132

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Prove that there exists NO norm such that $ f_n $ converges to $f$ iff $f_n$ converges to $f$ on compacta.

Published on 15 Apr 2026 - 16:36

score 416 · Answer 14 · 2026-04-14 10:37:59

416

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Pointwise convergence at every rational but not everywhere

Published on 14 Apr 2026 - 10:37

score 1.3k · Answer 15 · 2026-04-14 13:09:56

1.3k

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Show uniform convergence of $\sum_{k=1}^{\infty} x^k e^{-kx}$ where $x \in [0,\infty)$

Published on 14 Apr 2026 - 13:09

List Question

uniform convergence of functions over $\mathbb{R}^n$ implies integral convergence of functions with product

Pointwise convergence to infinity implies uniformly convergence?

Suppose $f_n\rightarrow f$ pointwise. Show that if each $f_n$ is continuous then $f$ is also continuous.

Uniform Convergence of Sequences

Help for example 19.7 in van der Vaart: show that a parametric class of functions with Lipschitz condition is Donsker

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

Is the convergence to the closure pointwise or uniform?

Uniform and absolute convergence of infinite trigonometric product

Simple questions about infinite products

If a sequence $(f_n)$ do not converge uniformly, then no subsequence of $(f_n)$ converge uniformly

Non zero continuous path $[0,1]\to \mathbb C$ has continuous logarithm

Uniform convergence of $f_n(x)=nx^{n-1}$ on $[0,1)$.

Prove that there exists NO norm such that $ f_n $ converges to $f$ iff $f_n$ converges to $f$ on compacta.

Pointwise convergence at every rational but not everywhere

Show uniform convergence of $\sum_{k=1}^{\infty} x^k e^{-kx}$ where $x \in [0,\infty)$

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