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Absolutely summable family

AbsolutelySummabledef

A family is absolutely summable when the sum of the norms converges. This is the hypothesis under which rearrangement is harmless and Fourier series converge uniformly.

def AbsolutelySummable {ι E : Type*} [NormedAddCommGroup E] (f : ι → E) : Prop :=
  Summable fun i => ‖f i‖

import Conjectura.Defs.Mathematics.Analysis.HarmonicAnalysis.AbsolutelySummable · maintainer — open · raw source

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