List questions from pointwise-convergence

Published on 02 Jan 2022 - 12:15

51

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Pointwise convergence of this function

Published on 02 Jan 2022 - 19:02

49

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The limit of sequence of functions

Published on 02 Jan 2022 - 19:57

1.8k

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If $(f_n')$ converges uniformly on an interval, does $(f_n)$ converge?

Published on 02 Jan 2022 - 23:22

141

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Why pointwise convergence does not imply uniform convergence?

Published on 08 Jan 2022 - 17:19

41

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misconception about pointwise/uniform convergence

Published on 13 Jan 2022 - 1:27

82

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Comparing different kinds of convergence

Published on 22 Jan 2022 - 23:33

46

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Test pointwise and uniform convergence of the following sequences of functions on $[0,1]$: $f_{j}=x^{j}-x^{j+1}$ and $f_{j}=x^{j}-x^{2j}$.

Published on 24 Jan 2022 - 15:50

61

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Limit under the sign of integral

Published on 29 Jan 2022 - 11:23

26

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Show the sequence uniformly converge to null function.

Published on 08 Feb 2022 - 11:28

56

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Only pointwise convergence or also uniform convergence?

Published on 14 Feb 2022 - 22:27

34

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How can the pointwise and uniform limits of sequences of functions defined by parts be treated?

Published on 15 Feb 2022 - 16:38

107

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necessary and sufficient conditions of $\frac{X_n}{a_n}\rightarrow0, \frac{S_n}{a_n}\rightarrow0$ and $\frac{max\{X_1,...,X_n\}}{a_n}\rightarrow0$.

Published on 20 Feb 2022 - 8:20

72

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If $\mu(A_n\Delta A)\to0$, why is $A=\bigcup_{n\ge1}\bigcap_{m\ge n}A_m$? I get that it only holds for a subsequence

Published on 23 Feb 2022 - 19:30

88

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Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

Published on 27 Feb 2022 - 14:43

List Question

$\lim_{n\to\infty} n^2 \int_{0}^{1} \frac{x\sin{x}}{1+(nx)^3} \, \mathrm{d}x$

Pointwise convergence of this function

The limit of sequence of functions

If $(f_n')$ converges uniformly on an interval, does $(f_n)$ converge?

Why pointwise convergence does not imply uniform convergence?

misconception about pointwise/uniform convergence

Comparing different kinds of convergence

Test pointwise and uniform convergence of the following sequences of functions on $[0,1]$: $f_{j}=x^{j}-x^{j+1}$ and $f_{j}=x^{j}-x^{2j}$.

Limit under the sign of integral

Show the sequence uniformly converge to null function.

Only pointwise convergence or also uniform convergence?

How can the pointwise and uniform limits of sequences of functions defined by parts be treated?

necessary and sufficient conditions of $\frac{X_n}{a_n}\rightarrow0, \frac{S_n}{a_n}\rightarrow0$ and $\frac{max\{X_1,...,X_n\}}{a_n}\rightarrow0$.

If $\mu(A_n\Delta A)\to0$, why is $A=\bigcup_{n\ge1}\bigcap_{m\ge n}A_m$? I get that it only holds for a subsequence

Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

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