Theorems · Definition · measure theory
MeasureTheory.Measure.everywherePosSubset
{α : Type u_1} → [TopologicalSpace α] → [inst : MeasurableSpace α] → MeasureTheory.Measure α → Set α → Set αThe everywhere positive subset of a set is the subset made of those points all of whose neighborhoods have positive measure inside the set.
- 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.
Cites7
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
- Set.ofPredproof · cited by 6,101
- nhdsWithinproof · cited by 1,912
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.everywherePosSubset_subsetstatement and proof · cited by 4
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_sdiffstatement · cited by 4
- MeasureTheory.Measure.everywherePosSubset_ae_eq_of_measure_ne_topstatement and proof · cited by 3
- IsClosed.everywherePosSubsetstatement and proof · cited by 2
- IsCompact.everywherePosSubsetstatement and proof · cited by 2
- MeasurableSet.everywherePosSubsetstatement and proof · cited by 2
- MeasureTheory.Measure.measure_eq_zero_of_subset_sdiff_everywherePosSubsetstatement and proof · cited by 2
- MeasureTheory.Measure.isEverywherePos_everywherePosSubset_of_measure_ne_topstatement and proof · cited by 2
- MeasureTheory.Measure.everywherePosSubset_ae_eqstatement and proof · cited by 1
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_diffstatement · cited by 0