Theorems · Definition · several complex variables

AnalyticOn

(𝕜 : Type u_1) →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [NormedSpace 𝕜 E] → [inst_3 : NormedAddCommGroup F] → [NormedSpace 𝕜 F] → (E → F) → Set E → Prop

f is analytic within s if it is analytic within s at each point of s. Note that this is weaker than AnalyticOnNhd 𝕜 f s, as f is allowed to be arbitrary outside s.

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

161 results in Mathlib

Foundations

Depth 166 from the axioms, rests on 3,366 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace