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Sequences and uniform convergence

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#real-analysis #sequences-and-series #uniform-convergence #sequence-of-function
485
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Find the pointwise limit and the uniform convergence of $f_n(x) = x(1-x^n)$ and $f_n(x) = \frac{nx}{n+2}$

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#real-analysis #uniform-convergence #sequence-of-function #pointwise-convergence
146
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Uniformly bounded sequence of functions

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#real-analysis #improper-integrals #sequence-of-function #pointwise-convergence
562
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Pointwise convergent, increasing sequence

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#real-analysis #uniform-convergence #sequence-of-function #absolute-continuity
75
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Integral of pointwise limit of functions is smaller than integral of each function

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#real-analysis #riemann-integration #sequence-of-function
150
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A function about continuous convergence i.e $f_n(x_n)\to f(x)$

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#real-analysis #normed-spaces #uniform-convergence #sequence-of-function
180
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Does locally uniform convergence preserve analyticity?

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#sequences-and-series #complex-analysis #uniform-convergence #sequence-of-function
137
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Limit of polynomial functions

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#real-analysis #calculus #sequences-and-series #sequence-of-function
245
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Sequence of continuous functions that has no convergent subsequence

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#real-analysis #general-topology #sequence-of-function
95
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Need a proof for a generalized sequence test.

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#real-analysis #analysis #convergence-divergence #sequence-of-function
106
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Open sets of linear functions with respect to a metric

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#real-analysis #sequences-and-series #general-topology #sequence-of-function
41
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Behavior of a sequence of uniformly continuous functions at the boundary of the interval

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#real-analysis #continuity #sequence-of-function
97
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Find a sequence $\left\{f_{n}\right\}$ of Borel measurable functions on $\mathbb{R}$ which...

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#integration #measure-theory #lebesgue-integral #lebesgue-measure #sequence-of-function
63
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Does the real number $\sup_{t∈(0,1)}θ(t)$ exist

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#real-analysis #sequences-and-series #limits #limsup-and-liminf #sequence-of-function
35
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Extension of almost everywhere convergent sequence of functions

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#real-analysis #measure-theory #sequence-of-function #almost-everywhere

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