Theorems · Theorem · real analysis

hasFTaylorSeriesUpToOn_univ_iff

∀ {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] {f : E → F}
  {n : WithTop ℕ∞} {p : E → FormalMultilinearSeries 𝕜 E F},
  HasFTaylorSeriesUpToOn n f p Set.univ ↔ HasFTaylorSeriesUpTo n f p

Defined in

Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries

Cited by

8 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace