List questions from pointwise-convergence

Published on 06 Oct 2020 - 10:06

72

Views

Prove $f_k(x)$ converges pointwise to $f$ on $\mathbb{R}$

Published on 06 Oct 2020 - 16:38

66

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Showing that a sequence of piecewise functions converges

Published on 08 Oct 2020 - 1:21

65

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Show convergence of this infinite product

Published on 10 Oct 2020 - 12:15

107

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LOTUS for non-continuous funtion

Published on 14 Oct 2020 - 23:29

196

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For $f_n$ a mollification of $f$, do we have $f_n \to f$ almost everywhere implies $\lim_{n\to \infty} ||f_n||_{L^2} = ||f||_{L^2}$?

Published on 20 Oct 2020 - 20:28

129

Views

When is a pointwise limit of a continuous function measurable?

Published on 21 Oct 2020 - 4:57

98

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Convergence of the series $\frac{1} {n} \sin(nx) $

Published on 29 Oct 2020 - 13:00

205

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Is the limit of a sequence of continuous functions bounded?

Published on 01 Nov 2020 - 16:25

328

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Finding a sequence of integrable functions on $[0,1]$ which is pointwise convergent to zero whose integrals increase without bound

Published on 04 Nov 2020 - 21:14

76

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Convergence of maximum points on compact sets

Published on 06 Nov 2020 - 15:52

40

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Showing $f_n(x) = \frac{nx}{1+\lvert{nx}\rvert}$ converges pointwise but not uniformly

Published on 10 Nov 2020 - 13:55

98

Views

sequence of functions, limits and integral

Published on 17 Nov 2020 - 3:47

110

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Sequence of compactly supported functions converging to rectangle

Published on 17 Nov 2020 - 19:03

61

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If $f_{n}\to f$ in $L^{2}$ and $f_{n}$ are absolutely continuous does $f_{n}\to f$ a.e?

Published on 19 Nov 2020 - 0:03

List Question

Why do we need topological spaces?

Prove $f_k(x)$ converges pointwise to $f$ on $\mathbb{R}$

Showing that a sequence of piecewise functions converges

Show convergence of this infinite product

LOTUS for non-continuous funtion

For $f_n$ a mollification of $f$, do we have $f_n \to f$ almost everywhere implies $\lim_{n\to \infty} ||f_n||_{L^2} = ||f||_{L^2}$?

When is a pointwise limit of a continuous function measurable?

Convergence of the series $\frac{1} {n} \sin(nx) $

Is the limit of a sequence of continuous functions bounded?

Finding a sequence of integrable functions on $[0,1]$ which is pointwise convergent to zero whose integrals increase without bound

Convergence of maximum points on compact sets

Showing $f_n(x) = \frac{nx}{1+\lvert{nx}\rvert}$ converges pointwise but not uniformly

sequence of functions, limits and integral

Sequence of compactly supported functions converging to rectangle

If $f_{n}\to f$ in $L^{2}$ and $f_{n}$ are absolutely continuous does $f_{n}\to f$ a.e?

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