Theorems · Theorem · functional analysis

hasFDerivAtFilter_iff_isLittleO

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : SeminormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {f' : E →L[𝕜] F} {L : Filter (E × E)},
  HasFDerivAtFilter f f' L ↔ (fun p => f p.1 - f p.2 - f' (p.1 - p.2)) =o[L] fun p => p.1 - p.2

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

5 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace