Theorems · Theorem · measure theory
MeasureTheory.Measure.IsOpenPosMeasure.open_pos
∀ {X : Type u_1} {inst : TopologicalSpace X} {m : MeasurableSpace X} {μ : MeasureTheory.Measure X}
[self : μ.IsOpenPosMeasure] (U : Set X), IsOpen U → U.Nonempty → μ U ≠ 0- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 6 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · 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
- ENNRealstatement · cited by 9,879
- Set.Nonemptystatement · cited by 2,627
- IsOpenstatement · cited by 2,400
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
Cited by6
Results whose statement or proof uses this declaration.
- IsOpen.measure_ne_zeroproof · cited by 6
- IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_AddHaarMeasureproof · cited by 1
- IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_HaarMeasureproof · cited by 1
- MeasureTheory.QuotientMeasureEqMeasurePreimage.haarMeasure_quotientproof · cited by 0
- MeasureTheory.Measure.IsOpenPosMeasure.comapproof · cited by 0