Theorems · Theorem · global analysis

Filter.EventuallyEq.hasLineDerivWithinAt_iff

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f₀ f₁ : E → F}
  {f' : F} {s : Set E} {x v : E},
  f₀ =ᶠ[nhdsWithin x s] f₁ → f₀ x = f₁ x → (HasLineDerivWithinAt 𝕜 f₀ f' s x v ↔ HasLineDerivWithinAt 𝕜 f₁ f' s x v)

Defined in

Mathlib.Analysis.Calculus.LineDeriv.Basic

Cited by

3 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace