List questions from uniform-convergence

Published on 11 Apr 2026 - 20:22

176

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Examples that show that covergen in the measure does not imply convergence almost everywhere?

Published on 11 Apr 2026 - 4:22

146

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How to show that series $\sum\frac{x}{1+n^2x}$is uniform convergent in $(t,1]$ where $t>0$ but not uniform convergent in $[0,1]$?

Published on 03 Jan 2016 - 12:09

442

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Prove or Disprove there is a sequence $f_n$ of continuous function on [0,1] such that for each x $ \in [0,1] $, $f_n(x)$ converges to $f(x)$

Published on 12 Apr 2026 - 8:42

211

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How to show that the Fourier's series of $f(x)=x$ uniformly converges?

Published on 13 Apr 2026 - 0:10

90

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Uniform convergence of $\frac{x^n}{1+x}$ and $\frac{x^n}{1+nx}$

Published on 06 Jan 2016 - 9:30

260

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Suppose $\int_0^1 f(x)x^kdx = 0$ for any nonnegative integer $k$. Show $f\equiv 0$ on $[0,1]$.

Published on 07 Jan 2016 - 3:18

898

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Prove a function is pointwise convergent

Published on 13 Apr 2026 - 16:52

349

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Is $f_n$ uniformly convergent?

Published on 11 Apr 2026 - 17:44

267

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Determine whether the functional series $\sum\frac1{(x+j)^2}$ and $(\sin\frac{x}{j})^j$ are pointwise and/or uniform convergent

Published on 09 Jan 2016 - 18:40

595

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Show a sequence of functions is pointwise but not uniformly convergent

Published on 12 Apr 2026 - 22:53

274

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Uniform convergence of $f_n = \frac{nx}{1+nx^2}$.

Published on 13 Apr 2026 - 7:49

243

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Convergence of the series (N.B.H.M)

Published on 10 Jan 2016 - 9:10

198

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Prove a functional series is pointwise and/or uniformly convergent

Published on 10 Jan 2016 - 14:31

63

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Determine whether a function series is uniformly convergent

Published on 11 Apr 2026 - 21:15

List Question

About the convergence of series and sequences of functions

Examples that show that covergen in the measure does not imply convergence almost everywhere?

How to show that series $\sum\frac{x}{1+n^2x}$is uniform convergent in $(t,1]$ where $t>0$ but not uniform convergent in $[0,1]$?

Prove or Disprove there is a sequence $f_n$ of continuous function on [0,1] such that for each x $ \in [0,1] $, $f_n(x)$ converges to $f(x)$

How to show that the Fourier's series of $f(x)=x$ uniformly converges?

Uniform convergence of $\frac{x^n}{1+x}$ and $\frac{x^n}{1+nx}$

Suppose $\int_0^1 f(x)x^kdx = 0$ for any nonnegative integer $k$. Show $f\equiv 0$ on $[0,1]$.

Prove a function is pointwise convergent

Is $f_n$ uniformly convergent?

Determine whether the functional series $\sum\frac1{(x+j)^2}$ and $(\sin\frac{x}{j})^j$ are pointwise and/or uniform convergent

Show a sequence of functions is pointwise but not uniformly convergent

Uniform convergence of $f_n = \frac{nx}{1+nx^2}$.

Convergence of the series (N.B.H.M)

Prove a functional series is pointwise and/or uniformly convergent

Determine whether a function series is uniformly convergent

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