Theorems · Definition · measure theory
MeasureTheory.Measure.IsEverywherePos
{α : Type u_1} → [TopologicalSpace α] → [inst : MeasurableSpace α] → MeasureTheory.Measure α → Set α → PropA set s is everywhere positive (also called self-supporting) with respect to a
measure μ if it has positive measure around each of its points, i.e., if all neighborhoods n
of points of s satisfy μ (s ∩ n) > 0.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- nhdsWithinproof · cited by 1,912
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.IsEverywherePos.of_forall_exists_nhds_eqstatement and proof · cited by 3
- IsOpen.isEverywherePosstatement · cited by 2
- MeasureTheory.Measure.IsEverywherePos.smul_measure_nnrealstatement and proof · cited by 2
- MeasureTheory.Measure.isEverywherePos_everywherePosSubset_of_measure_ne_topstatement · cited by 2
- MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePosstatement and proof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isMulLeftInvariantstatement and proof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isAddLeftInvariantstatement and proof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.smul_measurestatement and proof · cited by 1
- MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePosstatement and proof · cited by 1
- MeasureTheory.Measure.isEverywherePos_everywherePosSubsetstatement · cited by 0