Theorems · Theorem · functional analysis

fderivWithin_def

∀ (𝕜 : Type u_4) [inst : NontriviallyNormedField 𝕜] {E : Type u_5} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_6} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] (f : E → F) (s : Set E) (x : E),
  fderivWithin 𝕜 f s x =
    if HasFDerivWithinAt f 0 s x then 0 else if h : DifferentiableWithinAt 𝕜 f s x then Classical.choose h else 0

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

12 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace