Theorems · Theorem · functional analysis

HasFDerivAt.lim_real

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {F : Type u_2} [inst_2 : NormedAddCommGroup F]
  [inst_3 : NormedSpace ℝ F] {f : E → F} {f' : E →L[ℝ] F} {x : E},
  HasFDerivAt f f' x → ∀ (v : E), Filter.Tendsto (fun c => c • (f (x + c⁻¹ • v) - f x)) Filter.atTop (nhds (f' v))

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace