Theorems · Inductive type · measure theory
MeasureTheory.IsProbabilityMeasure
{α : Type u_1} → {m0 : MeasurableSpace α} → MeasureTheory.Measure α → PropA measure μ is called a probability measure if μ univ = 1.
- Cited by
- 392 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
Cited by404
Results whose statement or proof uses this declaration.
- MeasureTheory.IsProbabilityMeasure.measure_univstatement and proof · cited by 135
- MeasureTheory.ProbabilityMeasureproof · cited by 127
- MeasureTheory.Measure.infinitePiproof · cited by 48
- MeasureTheory.probReal_univstatement and proof · cited by 39
- MeasureTheory.TendstoInDistributionstatement · cited by 19
- MeasureTheory.Measure.isProbabilityMeasure_mapstatement and proof · cited by 19
- MeasureTheory.IsProbabilityMeasure.ne_zerostatement and proof · cited by 17
- ProbabilityTheory.iIndepFun.isProbabilityMeasurestatement · cited by 14
- MeasureTheory.average_eq_integralstatement and proof · cited by 11
- ProbabilityTheory.HasGaussianLaw.isProbabilityMeasurestatement · cited by 8
- MeasureTheory.piContentstatement and proof · cited by 8
- ProbabilityTheory.Kernel.iIndep.ae_isProbabilityMeasurestatement · cited by 7
Showing the 200 most cited of 404.