Theorems · Theorem · functional analysis

hasFDerivWithinAt_iff_isLittleOTVS

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] {f : E → F} {f' : E →L[𝕜] F} {x : E} {s : Set E},
  HasFDerivWithinAt f f' s x ↔ (fun x' => f x' - f x - f' (x' - x)) =o[𝕜; nhdsWithin x s] fun x' => x' - x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

4 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace