Theorems · Theorem · measure theory
MeasureTheory.Measure.measure_pos_of_nonempty_interior
∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure]
{s : Set X}, (interior s).Nonempty → 0 < μ s- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 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
- ENNRealstatement · cited by 9,879
- Set.Nonemptystatement and proof · cited by 2,627
- interiorstatement and proof · cited by 714
- LT.lt.trans_leproof · cited by 678
- MeasureTheory.measure_monoproof · cited by 338
- interior_subsetproof · cited by 171
- isOpen_interiorproof · cited by 130
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarMeasure_uniqueproof · cited by 9
- MeasureTheory.Measure.haarMeasure_uniqueproof · cited by 4
- MeasureTheory.Measure.measure_pos_of_mem_nhdsproof · cited by 3