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Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.
real-analysis
functional-analysis
arzela-ascoli
Given a bounded sequence in $L^1([a,b])$, is $(t\mapsto \int_a^t f_n \,\mathrm d\lambda)_n$ equicontinuous?
functional-analysis
lp-spaces
equicontinuity
arzela-ascoli
Is the integral operator $I: L^1([0,1])\to L^1([0,1]), f\mapsto (x\mapsto \int_0^x f \,\mathrm d\lambda)$ compact?
functional-analysis
compactness
lp-spaces
compact-operators
arzela-ascoli
Arzelà–Ascoli $\implies$ Dini's theorem
real-analysis
functional-analysis
analysis
arzela-ascoli
Variation of Ascoli-Arzelà theorem for $C^1$ functions
functional-analysis
compactness
arzela-ascoli
Sequence of contraction mapping and convergence of fixed point
functional-analysis
fixed-point-theorems
contraction-operator
arzela-ascoli
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