Theorems · Theorem · measure theory
MeasureTheory.IsProbabilityMeasure.measure_univ
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [self : MeasureTheory.IsProbabilityMeasure μ],
μ Set.univ = 1- Cited by
- 135 results in Mathlib
- Foundations
- Depth 170 from the axioms, rests on 4,584 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.univstatement · cited by 3,945
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
Cited by135
Results whose statement or proof uses this declaration.
- MeasureTheory.probReal_univproof · cited by 39
- MeasureTheory.lintegral_dirac'proof · cited by 19
- MeasureTheory.Measure.isProbabilityMeasure_mapproof · cited by 19
- MeasureTheory.IsProbabilityMeasure.ne_zeroproof · cited by 17
- MeasureTheory.lintegral_diracproof · cited by 13
- MeasureTheory.average_eq_integralproof · cited by 11
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- ProbabilityTheory.HasSubgaussianMGF_iff_kernelproof · cited by 9
- ProbabilityTheory.iIndepFun_iff_map_fun_eq_pi_mapproof · cited by 6
- MeasureTheory.laverage_eq_lintegralproof · cited by 6
- ProbabilityTheory.Kernel.indep_bot_rightproof · cited by 5
- MeasureTheory.measurePreserving_evalproof · cited by 5