Theorems · Theorem · global analysis

HasFDerivAtFilter.tendsto_nhds

∀ {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} [ContinuousAdd E] [ContinuousSMul 𝕜 E]
  [ContinuousAdd F] [ContinuousSMul 𝕜 F] {L : Filter E},
  L ≤ nhds x → HasFDerivAtFilter f f' (L ×ˢ pure x) → Filter.Tendsto f L (nhds (f x))

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMulContinuousAddContinuousSMul