Theorems · Inductive type · measure theory
HasBesicovitchCovering
(α : Type u_1) → [MetricSpace α] → Prop
A metric space has the Besicovitch covering property if there exist N and τ > 1 such that
there are no satellite configurations of parameter τ with N+1 points. This is the condition that
guarantees that the measurable Besicovitch covering theorem holds. It is satisfied by
finite-dimensional real vector spaces.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MetricSpacestatement · cited by 1,684
Cited by12
Results whose statement or proof uses this declaration.
- Besicovitch.vitaliFamilystatement and proof · cited by 5
- Besicovitch.tendsto_filterAtstatement and proof · cited by 4
- HasBesicovitchCovering.no_satelliteConfigstatement and proof · cited by 2
- Besicovitch.ae_tendsto_measure_inter_div_of_measurableSetstatement and proof · cited by 2
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxstatement and proof · cited by 1
- Besicovitch.ae_tendsto_measure_inter_divstatement and proof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_lestatement and proof · cited by 1
- Besicovitch.exists_disjoint_closedBall_covering_aestatement and proof · cited by 1
- Besicovitch.exists_disjoint_closedBall_covering_ae_auxstatement and proof · cited by 1
- HasBesicovitchCovering.casesOnstatement and proof · cited by 0
- HasBesicovitchCovering.recOnstatement and proof · cited by 0
- Besicovitch.ae_tendsto_rnDerivstatement and proof · cited by 0