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Prove $\{f_{k}\}$ converges uniformly on $[a,b]$.

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#real-analysis #sequences-and-series #uniform-convergence #cauchy-sequences
191
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Does pointwise converge imply uniform convergence in some interval?

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#real-analysis #examples-counterexamples #uniform-convergence #pointwise-convergence
67
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Does pointwise convergence of continuous functions imply uniform convergence in some interval?

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#real-analysis #uniform-convergence #pointwise-convergence
65
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Uniform Convergence on Standard Probability Space

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#probability-theory #uniform-convergence #product-space
71
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Confusion about the proof of uniform convergence

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#real-analysis #metric-spaces #uniform-convergence #cauchy-sequences #complete-spaces
101
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On the classic example of the sequence $f_n=x^n$

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#real-analysis #sequences-and-series #uniform-convergence #cauchy-sequences
175
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uniformly convergence to discontinuous function.

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#uniform-convergence
63
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Pointwise convergence of a series of function.

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#real-analysis #sequences-and-series #analysis #uniform-convergence #sequence-of-function
108
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Does $(f_n)$ converge uniformly on $[0,1]$?

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#real-analysis #uniform-convergence
56
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Limit of integral of $\frac{2nx^{n-1}}{1+x},\, x\in [0,1]$

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#integration #uniform-convergence #sequence-of-function
34
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bounds on matrix power

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#linear-algebra #matrices #eigenvalues-eigenvectors #uniform-convergence
1.2k
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Prove $g(x) = \sum_{k=0}^\infty \frac{(-1)^k}{2k+1}\,x^{2k+1}$ converges uniformly on [-1,1]

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#real-analysis #sequences-and-series #uniform-convergence #solution-verification
64
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Prove point-wise and uniform convergence of function (Carothers 10.9.f)

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#real-analysis #functional-analysis #uniform-convergence #pointwise-convergence
47
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Where is compactness used in the following exercise

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#metric-spaces #compactness #uniform-convergence
86
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Evaluate if a series converges to a continuous function

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#real-analysis #calculus #sequences-and-series #convergence-divergence #uniform-convergence

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