Theorems · Theorem · real analysis

LipschitzWith.ae_differentiableAt_real

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [FiniteDimensional ℝ V] {C : NNReal}
  {f : ℝ → V}, LipschitzWith C f → ∀ᵐ (x : ℝ), DifferentiableAt ℝ f x

A real Lipschitz function into a finite-dimensional real vector space is differentiable almost everywhere. For the general Rademacher theorem assuming that the source space is finite dimensional, see LipschitzWith.ae_differentiableAt.

Defined in

Mathlib.Analysis.BoundedVariation

Cited by

1 results in Mathlib

Foundations

Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFiniteDimensional