Theorems · Theorem · measure theory
MeasureTheory.Measure.count_ne_zero_iff
∀ {α : Type u_1} [inst : MeasurableSpace α] {s : Set α}, MeasureTheory.Measure.count s ≠ 0 ↔ s.Nonempty- Defined in
- Mathlib.MeasureTheory.Measure.Count
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Nonemptystatement · cited by 2,627
- Iff.notproof · cited by 489
- Set.nonempty_iff_ne_emptyproof · cited by 96
- MeasureTheory.Measure.countstatement · cited by 60
- MeasureTheory.Measure.count_eq_zero_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.uniformOn_selfproof · cited by 2
- ProbabilityTheory.isProbabilityMeasure_uniformOnproof · cited by 2
- MeasureTheory.Measure.count_ne_zeroproof · cited by 1
- ProbabilityTheory.isProbabilityMeasure_uniformOn'proof · cited by 0