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Theorems · Theorem · measure theory

MeasureTheory.Measure.count_ne_zero

∀ {α : Type u_1} [inst : MeasurableSpace α] {s : Set α}, s.Nonempty → MeasureTheory.Measure.count s ≠ 0

Alias of the reverse direction of MeasureTheory.Measure.count_ne_zero_iff.

Defined in
Mathlib.MeasureTheory.Measure.Count
Cited by
1 results in Mathlib
Foundations
Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.uniformOn_disjoint_union · cited by 1ProbabilityTheory.uniform…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.Nonempty · cited by 2627Set.NonemptyMeasureTheory.Measure.count · cited by 60Measure.countMeasureTheory.Measure.count_ne_zero_iff · cited by 4Measure.count_ne_zero_iffMeasure.count_ne_zeroCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.