Theorems · Theorem · real analysis
LipschitzWith.ae_lineDifferentiableAt
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
{C : NNReal} {f : E → ℝ} {μ : MeasureTheory.Measure E} [FiniteDimensional ℝ E] [μ.IsAddHaarMeasure],
LipschitzWith C f → ∀ (v : E), ∀ᵐ (p : E) ∂μ, LineDifferentiableAt ℝ f p v- Defined in
- Mathlib.Analysis.Calculus.Rademacher
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idproof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommGroupproof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NontriviallyNormedFieldproof · cited by 8,742
- ContinuousLinearMapproof · cited by 5,352
- NNRealstatement and proof · cited by 4,310
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mulproof · cited by 1
- LipschitzWith.ae_exists_fderiv_of_countableproof · cited by 1
- LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'proof · cited by 1