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Theorems · Theorem · complex analysis

Complex.re_tsum

∀ {α : Type u_1} {L : SummationFilter α} [L.NeBot] {f : α → ℂ},
  Summable f L → (∑'[L] (a : α), f a).re = ∑'[L] (a : α), (f a).re
Defined in
Mathlib.Analysis.Complex.Basic
Cited by
2 results in Mathlib
Foundations
Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SummationFilter.NeBot
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DirichletCharacter.norm_LSeries_product_ge_one · cited by 1DirichletCharacter.norm_L…ArithmeticFunction.vonMangoldt.LFunctionResidueClassAux_real · cited by 1vonMangoldt.LFunctionResi…Real · cited by 25697RealComplex · cited by 5565Complextsum · cited by 1148tsumComplex.re · cited by 882Complex.reSummable · cited by 778SummableSummationFilter · cited by 607SummationFilterSummationFilter.NeBot · cited by 130SummationFilter.NeBotRCLike.re_tsum · cited by 1RCLike.re_tsumComplex.re_tsumCITED BYCITES

Cites8

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Cited by2

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