List questions from pointwise-convergence

Published on 04 Apr 2021 - 16:12

103

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Prove that there exists a countable collection of measurable sets $\{A_n: n=0,1,2,3...\}$ such that $f_n\rightarrow f$ on $A_n$ and $m(\cup A_n)=1$.

Published on 05 Apr 2021 - 1:38

77

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$\lim\limits_{n\to\infty}\frac{a^n}{1+na}$

Published on 09 Apr 2021 - 11:58

40

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Proving an inequality absolute value

Published on 23 Feb 2026 - 22:25

116

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Prove convergence of the power series $\sum_{n=1}^\infty \frac{x^n}{\log(n+2)}$

Published on 10 Apr 2021 - 9:26

47

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$f_n(x) = \frac{x+x^2}{n}$ is not uniformly convergent

Published on 12 Apr 2021 - 16:50

164

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Convergence of a power series at an endpoint

Published on 16 Apr 2021 - 3:04

53

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Uniform and pointwise convergence of function series.

Published on 16 Apr 2021 - 8:33

113

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An interesting problem from Durrett or Chung's book

Published on 17 Apr 2021 - 1:31

68

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Limit of monotonic increasing functions is again montonic increasing

Published on 17 Apr 2021 - 16:59

890

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Finding $f$ s.t. the sequence of functions $f_n(x)=f (x − a_n )$ is not a.e. convergent to $f$

Published on 17 Apr 2021 - 19:08

255

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Converge pointwise but not uniformly a problem from Axler 2020

Published on 21 Apr 2021 - 20:33

648

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how can I define uniform convergence in topological spaces, and also the concept of convergent series without talking about nets?

Published on 26 Apr 2021 - 0:38

34

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Limit Proof (Find Sufficiently Large N)

Published on 27 Apr 2021 - 2:34

55

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Can we construct a counterexample that satifies the conditions?

Published on 29 Apr 2021 - 15:00

List Question

Convergent pointwise inequality

Prove that there exists a countable collection of measurable sets $\{A_n: n=0,1,2,3...\}$ such that $f_n\rightarrow f$ on $A_n$ and $m(\cup A_n)=1$.

$\lim\limits_{n\to\infty}\frac{a^n}{1+na}$

Proving an inequality absolute value

Prove convergence of the power series $\sum_{n=1}^\infty \frac{x^n}{\log(n+2)}$

$f_n(x) = \frac{x+x^2}{n}$ is not uniformly convergent

Convergence of a power series at an endpoint

Uniform and pointwise convergence of function series.

An interesting problem from Durrett or Chung's book

Limit of monotonic increasing functions is again montonic increasing

Finding $f$ s.t. the sequence of functions $f_n(x)=f (x − a_n )$ is not a.e. convergent to $f$

Converge pointwise but not uniformly a problem from Axler 2020

how can I define uniform convergence in topological spaces, and also the concept of convergent series without talking about nets?

Limit Proof (Find Sufficiently Large N)

Can we construct a counterexample that satifies the conditions?

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