Theorems · Theorem · measure theory
MeasureTheory.probReal_univ
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsProbabilityMeasure μ],
μ.real Set.univ = 1- Cited by
- 39 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univstatement · cited by 3,945
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
Cited by39
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_diracproof · cited by 20
- ProbabilityTheory.integral_id_multivariateGaussianproof · cited by 5
- MeasureTheory.integral_dirac'proof · cited by 4
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- ProbabilityTheory.iIndepFun.mgf_sum₀proof · cited by 3
- orthonormal_fourierproof · cited by 3
- ProbabilityTheory.covariance_add_const_leftproof · cited by 3
- ProbabilityTheory.variance_add_constproof · cited by 2
- InformationTheory.integrable_llr_compProd_iffproof · cited by 2
- ProbabilityTheory.covariance_eq_subproof · cited by 2
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2
- MeasureTheory.measureReal_abs_gt_le_integral_charFunproof · cited by 2