Theorems · Theorem · real analysis
LipschitzWith.locallyIntegrable_lineDeriv
∀ {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), MeasureTheory.LocallyIntegrable (fun x => lineDeriv ℝ f x v) μ- Defined in
- Mathlib.Analysis.Calculus.Rademacher
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NNRealstatement and proof · cited by 4,310
- FiniteDimensionalstatement and proof · cited by 1,854
- BorelSpacestatement and proof · cited by 1,602
- le_topproof · cited by 411
- LipschitzWithstatement and proof · cited by 316
- MeasureTheory.Measure.IsAddHaarMeasurestatement and proof · cited by 255
- MeasureTheory.LocallyIntegrablestatement · cited by 90
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzWith.ae_lineDeriv_sum_eqproof · cited by 1