List questions from pointwise-convergence

Published on 13 Apr 2026 - 10:03

60

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

Published on 13 Apr 2026 - 12:07

38

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

Published on 16 Apr 2026 - 20:04

32

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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 13 Apr 2026 - 16:59

338

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Convergence of Integrals implies almost everywhere convergence of functions

Published on 11 Apr 2026 - 7:57

33

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Convergence of measurable functions by two conditions

Published on 15 Apr 2026 - 0:53

66

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

Published on 16 Apr 2026 - 2:27

99

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Pointwise convergence and $L^2$ convergence.

Published on 15 Apr 2026 - 7:32

65

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Uniform and pointwise convergence of a real function.

Published on 13 Apr 2026 - 18:15

87

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

Published on 15 Apr 2026 - 12:19

167

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

Published on 14 Apr 2026 - 13:51

44

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

Published on 14 Apr 2026 - 4:38

142

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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 16 Apr 2026 - 0:37

47

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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 15 Apr 2026 - 9:06

70

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

Published on 15 Apr 2026 - 21:28

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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