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Theorems · Theorem · several complex variables

AnalyticOnNhd.add

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f g : E → F} {s : Set E},
  AnalyticOnNhd 𝕜 f s → AnalyticOnNhd 𝕜 g s → AnalyticOnNhd 𝕜 (f + g) s
Defined in
Mathlib.Analysis.Analytic.Constructions
Cited by
0 results in Mathlib
Foundations
Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldAnalyticOnNhd · cited by 206AnalyticOnNhdAnalyticAt.add · cited by 11AnalyticAt.addAnalyticOnNhd.addCITED BYCITES

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