List questions from pointwise-convergence

Published on 24 Nov 2021 - 19:56

57

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Uniform convergence when $a \lt b$ but not if $a \geq b$

Published on 25 Nov 2021 - 22:34

36

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$f_n^\alpha(x) = n^\alpha x^n$ converges almost everywhere

Published on 26 Nov 2021 - 14:27

29

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Is it true that $ \Im ( \sum_{k=0}^\infty z_k ) = \sum_{k=0}^\infty \Im( z_k)$ and $\Re ( \sum_{k=0}^\infty z_k )= \sum_{k=0}^\infty \Re( z_k) $?

Published on 03 Dec 2021 - 16:58

335

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Convergence of Integrals implies almost everywhere convergence of functions

Published on 06 Dec 2021 - 21:53

30

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Convergence of measurable functions by two conditions

Published on 07 Dec 2021 - 21:05

63

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$a_{n+1}=a_{n}+\frac{1}{n^{2}} a_{n-1}$, for $n \geq 2$

Published on 08 Dec 2021 - 18:47

96

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Pointwise convergence and $L^2$ convergence.

Published on 12 Dec 2021 - 17:02

62

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Uniform and pointwise convergence of a real function.

Published on 15 Dec 2021 - 5:37

84

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$\int (f-g)\phi^{1/n}=0$ implies $f=g$ ae.

Published on 24 Dec 2021 - 3:33

164

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Question on Egorov's Theorem: How do you find such $E_{\epsilon}$ sets?

Published on 26 Dec 2021 - 21:17

42

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To show that a recursively defined sequence of functions converges pointwise to $0$.

Published on 30 Dec 2021 - 0:32

139

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To find a sequence on $L^1$-norm equal to 2, converging a.e. to a function of $L^1$norm equal to 1.

Published on 31 Dec 2021 - 2:25

45

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Why doesn't proving $f\in L^2(S^1)$ can be expanded into a Fourier series imply pointwise convergence of continuous functions?

Published on 01 Jan 2022 - 17:42

67

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$\lim_{n\rightarrow \infty} \int_D f_n d\mu=\int_D fd\mu$ when $f$ is integrable

Published on 02 Jan 2022 - 10:54

List Question

Limit of the integral of a measurable function

Uniform convergence when $a \lt b$ but not if $a \geq b$

$f_n^\alpha(x) = n^\alpha x^n$ converges almost everywhere

Is it true that $ \Im ( \sum_{k=0}^\infty z_k ) = \sum_{k=0}^\infty \Im( z_k)$ and $\Re ( \sum_{k=0}^\infty z_k )= \sum_{k=0}^\infty \Re( z_k) $?

Convergence of Integrals implies almost everywhere convergence of functions

Convergence of measurable functions by two conditions

$a_{n+1}=a_{n}+\frac{1}{n^{2}} a_{n-1}$, for $n \geq 2$

Pointwise convergence and $L^2$ convergence.

Uniform and pointwise convergence of a real function.

$\int (f-g)\phi^{1/n}=0$ implies $f=g$ ae.

Question on Egorov's Theorem: How do you find such $E_{\epsilon}$ sets?

To show that a recursively defined sequence of functions converges pointwise to $0$.

To find a sequence on $L^1$-norm equal to 2, converging a.e. to a function of $L^1$norm equal to 1.

Why doesn't proving $f\in L^2(S^1)$ can be expanded into a Fourier series imply pointwise convergence of continuous functions?

$\lim_{n\rightarrow \infty} \int_D f_n d\mu=\int_D fd\mu$ when $f$ is integrable

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