Theorems · Theorem · real analysis

HasFTaylorSeriesUpToOn.analyticOn

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {f : E → F} {p : E → FormalMultilinearSeries 𝕜 E F},
  HasFTaylorSeriesUpToOn ⊤ f p s → AnalyticOn 𝕜 (fun x => p x 0) s → AnalyticOn 𝕜 f s

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

2 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace