Theorems · Theorem · real analysis
LipschitzWith.memLp_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},
LipschitzWith C f → ∀ (v : E), MeasureTheory.MemLp (fun x => lineDeriv ℝ f x v) ⊤ μ- Defined in
- Mathlib.Analysis.Calculus.Rademacher
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- BorelSpacestatement and proof · cited by 1,602
- NNReal.toRealproof · cited by 1,260
- Filter.Eventually.of_forallproof · cited by 526
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzWith.locallyIntegrable_lineDerivproof · cited by 1
- LipschitzWith.ae_lineDeriv_sum_eqproof · cited by 1