Theorems · Theorem · functional analysis

HasFDerivAt.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} {x : E}, HasFDerivAt f f' x → (fun x' => f x' - f x - f' (x' - x)) =o[nhds x] fun x' => x' - x

Alias of the forward direction of hasFDerivAt_iff_isLittleO.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

2 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace