List questions from pointwise-convergence

Published on 28 Mar 2019 - 20:20

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If $f_n\to f$ pointwise, $f$ is continuous and $f$ is continuous, then $f_n \to f$ uniformly.

Published on 30 Mar 2019 - 15:55

51

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How to negate this statement

Published on 02 Apr 2019 - 19:26

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Convergence of $\sum_{n=1}^{\infty}\frac{x}{[(n-1)x+1](nx+1)}$

Published on 06 Apr 2019 - 11:14

63

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is $f_n=x^{-n} $convergent point wise? uniformly?

Published on 14 Apr 2019 - 22:49

24

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Does taking the limit in one argument preserve regularity in another argument?

Published on 15 Apr 2019 - 16:52

198

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Rigorous construction of the pointwise limit of a sequence of random variables

Published on 18 Apr 2019 - 10:04

1.4k

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Pointwise convergence implies convergence in the norm

Published on 23 Apr 2019 - 17:23

42

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A precise definition for a sequence of functions that "Converge Pointwise, but not Uniformly"

Published on 25 Apr 2019 - 0:28

47

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Let $g_n : [0,\frac{ 1} {2} ] → \mathbb R$ by $g_1 = g$ and $g_{n+1}(t) = \int_0^t g_n(s) ds,$ for all $n ≥ 1.$ Show that $\lim_{n→∞} n!g_n(t) = 0,$

Published on 26 Apr 2019 - 16:15

4k

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Pointwise convergence of $x^n$ in $[0,1]$

Published on 27 Apr 2019 - 18:12

36

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Pointwise convergence of $h_{n}(x)$ on [0,$\infty$)

Published on 27 Apr 2019 - 21:09

159

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Show uniform convergence and pointwise convergence for $\sum_{n=1}^ \infty \frac{z^ {n-1}}{(1-z^n)(1-z^ {n+1})}$

Published on 28 Apr 2019 - 9:46

203

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Prove that $(f_n)$, $f_n =x^n$, $x \in (0,1)$ is not uniformly convergent on $(0,1)$

Published on 03 May 2019 - 19:15

21

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Uniform boundedness of pointwise convergent functions

Published on 06 May 2019 - 10:54

List Question

Uniform convergence of the following series:

If $f_n\to f$ pointwise, $f$ is continuous and $f$ is continuous, then $f_n \to f$ uniformly.

How to negate this statement

Convergence of $\sum_{n=1}^{\infty}\frac{x}{[(n-1)x+1](nx+1)}$

is $f_n=x^{-n} $convergent point wise? uniformly?

Does taking the limit in one argument preserve regularity in another argument?

Rigorous construction of the pointwise limit of a sequence of random variables

Pointwise convergence implies convergence in the norm

A precise definition for a sequence of functions that "Converge Pointwise, but not Uniformly"

Let $g_n : [0,\frac{ 1} {2} ] → \mathbb R$ by $g_1 = g$ and $g_{n+1}(t) = \int_0^t g_n(s) ds,$ for all $n ≥ 1.$ Show that $\lim_{n→∞} n!g_n(t) = 0,$

Pointwise convergence of $x^n$ in $[0,1]$

Pointwise convergence of $h_{n}(x)$ on [0,$\infty$)

Show uniform convergence and pointwise convergence for $\sum_{n=1}^ \infty \frac{z^ {n-1}}{(1-z^n)(1-z^ {n+1})}$

Prove that $(f_n)$, $f_n =x^n$, $x \in (0,1)$ is not uniformly convergent on $(0,1)$

Uniform boundedness of pointwise convergent functions

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