Theorems · Theorem · real analysis

Filter.EventuallyEq.ftaylorSeriesWithin

∀ (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 f₁ : E → F} {x : E},
  f₁ =ᶠ[nhdsWithin x s] f → ftaylorSeriesWithin 𝕜 f₁ s =ᶠ[nhdsWithin x s] ftaylorSeriesWithin 𝕜 f s

If two functions agree in a neighborhood within s, then so do their Taylor series.

Defined in

Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries

Cited by

0 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace