Theorems · Theorem · real analysis

LocallyBoundedVariationOn.ae_differentiableAt

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [FiniteDimensional ℝ V] {f : ℝ → V},
  LocallyBoundedVariationOn f Set.univ → ∀ᵐ (x : ℝ), DifferentiableAt ℝ f x

A real function into a finite-dimensional real vector space with bounded variation is differentiable almost everywhere.

Defined in

Mathlib.Analysis.BoundedVariation

Cited by

1 results in Mathlib

Foundations

Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensional