Theorems · Theorem · complex analysis

MeromorphicOn.fun_smul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {R : Type u_4} [inst_3 : NormedRing R] [inst_4 : Module R E] [IsBoundedSMul R E]
  {U : Set 𝕜} [inst_6 : NormedAlgebra 𝕜 R] [IsScalarTower 𝕜 R E] {s : 𝕜 → R},
  MeromorphicOn s U → ∀ {f : 𝕜 → E}, MeromorphicOn f U → MeromorphicOn (fun i => s i • f i) U

Eta-expanded form of MeromorphicOn.smul

Defined in

Mathlib.Analysis.Meromorphic.Basic

Cited by

0 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingModuleIsBoundedSMulNormedAlgebraIsScalarTower