Theorems · Definition · functional analysis

HasFDerivAt

{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] → (E → F) → (E →L[𝕜] F) → E → Prop

A function f has the continuous linear map f' as derivative at x if f x' = f x + f' (x' - x) + o (x' - x) when x' tends to x.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Defs

Cited by

350 results in Mathlib

Foundations

Depth 60 from the axioms, rests on 888 definitions · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpace