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15
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Uniform convergence - Length of graph

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#sequences-and-series #analysis #graphing-functions #uniform-convergence #sequence-of-function
156
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Arzela-Ascoli generalisation uniform or pointwise convergence?

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#real-analysis #convergence-divergence #metric-spaces #uniform-convergence #arzela-ascoli
117
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Doubt in theorem 7.11 of Baby Rudin regarding completeness.

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#real-analysis #uniform-convergence
48
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Show uniform convergence using continuous function

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#compactness #uniform-convergence #pointwise-convergence #equicontinuity #arzela-ascoli
251
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Weak convergence using convergence in distribution

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#probability #probability-distributions #convergence-divergence #uniform-convergence #uniform-distribution
97
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Uniform convergence for a function on rational numbers

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#real-analysis #limits #uniform-convergence
103
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A contradiction to Dini's theorem?

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#compactness #uniform-convergence
76
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$\lim_{t \rightarrow 0} \frac{1}{2t} \int_{b-t}^{b+t} |f- \frac{1}{2t} \int_{b-t}^{b+t} f| = 0$

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#real-analysis #analysis #measure-theory #lebesgue-integral #uniform-convergence
28
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How to show $\sup_{\theta\in(0,1)}|\log(\theta)(\bar{X}_n-\mathbb{E}[X_i])|\xrightarrow[]{p}0$?

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#probability-theory #uniform-convergence
52
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If $G_n(z)=(z-z_0)g_n(z)$ converges uniformly to $f(z)-f(z_0)$, what can I say about the convergence of $g_n(z)$?

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#complex-analysis #uniform-convergence
38
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How to prove that a function sequence converges uniformly and to find an integral

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#uniform-convergence
39
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What is the interval of convergence for $\sum_{n=1}^\infty \frac{2^nx^{2n}}{n^2}$

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#real-analysis #summation #uniform-convergence
254
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Show strong operator convergence

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#functional-analysis #uniform-convergence #strong-convergence
79
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Prove that, $\int_a^b f(x)\ \text{d}\alpha=\sum_{n=1}^{\infty}\int_a^b f_n(x)\ \text{d}\alpha.$

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#real-analysis #uniform-convergence
94
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A Borel-Cantelli question

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#probability-theory #uniform-convergence #borel-cantelli-lemmas

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