Theorems · Theorem · probability
ProbabilityTheory.HasGaussianLaw.isProbabilityMeasure
∀ {Ω : Type u_1} {E : Type u_2} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} [inst : TopologicalSpace E]
[inst_1 : AddCommMonoid E] [inst_2 : Module ℝ E] [mE : MeasurableSpace E] {X : Ω → E},
ProbabilityTheory.HasGaussianLaw X P → MeasureTheory.IsProbabilityMeasure P- Cited by
- 8 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidstatement and proof · cited by 12,281
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.IsProbabilityMeasurestatement · cited by 392
- ProbabilityTheory.HasGaussianLawstatement and proof · cited by 67
- MeasureTheory.Measure.isProbabilityMeasure_of_mapproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussianProcess.isProbabilityMeasureproof · cited by 6
- ProbabilityTheory.IndepFun.hasGaussianLawproof · cited by 4
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_strongDualproof · cited by 3
- ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_strongDualproof · cited by 3
- ProbabilityTheory.HasIndepIncrements.isGaussianProcessproof · cited by 1
- ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_subproof · cited by 1
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_evalproof · cited by 0
- ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_evalproof · cited by 0