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Uniform convergence NBHM(2019)

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#uniform-convergence
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Uniform or pointwise convergence of a sequence of functions

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#real-analysis #proof-verification #uniform-convergence #sequence-of-function #pointwise-convergence
54
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Puntual and uniform convergence of function

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#sequences-and-series #convergence-divergence #uniform-convergence #sequence-of-function
120
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Prove that the sequence is pointwise convergent.

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#real-analysis #calculus #functions #convergence-divergence #uniform-convergence
42
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Uniform convergence of a sequence of functions 4

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#sequences-and-series #convergence-divergence #uniform-convergence #supremum-and-infimum #sequence-of-function
37
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Uniform convergence of a seriesobtained by dominating it with another series

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#sequences-and-series #convergence-divergence #uniform-convergence
37
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Computing $S_n(x)$, the partial sum of a series explicitly

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#sequences-and-series #summation #uniform-convergence #telescopic-series
91
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Defining a subset of uniform convergence of a succession of functions

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#real-analysis #convergence-divergence #uniform-convergence
59
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I have a question on infinite products

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#sequences-and-series #complex-analysis #uniform-convergence #infinite-product
538
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Supremum of uniformly converges functions goes to the supremum of the limiting function

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#limits #uniform-convergence #supremum-and-infimum
108
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Calculate $\lim_{n \to \infty} \int_0^1nx^nf(x)dx$.

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#real-analysis #calculus #analysis #uniform-convergence #sequence-of-function
100
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How to compute the $n^{th}$ partial sum of a series?

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#sequences-and-series #uniform-convergence #uniform-continuity #telescopic-series
61
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Uniform convergence of $x^n$ on interval $[0,b]$ for $0 \leq b < 1$.

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#uniform-convergence
31
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Suppose $\hat F_n(y)\overset{p}\to F(y)$, can we obtain $\sup_y|\hat F_n(y)-F(y)|\overset{p}\to0$?

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#probability #probability-theory #probability-distributions #convergence-divergence #uniform-convergence
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If a sequence of functions $f_n$ converges uniformly to $f$, does this imply $f_n$ is continuous? How to prove?

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#real-analysis #continuity #uniform-convergence

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