Theorems · Theorem · probability
ProbabilityTheory.HasGaussianLaw.isGaussian_map
∀ {Ω : Type u_1} {E : Type u_2} {mΩ : MeasurableSpace Ω} [inst : TopologicalSpace E] [inst_1 : AddCommMonoid E]
[inst_2 : Module ℝ E] [mE : MeasurableSpace E] {X : Ω → E} {P : MeasureTheory.Measure Ω},
ProbabilityTheory.HasGaussianLaw X P → ProbabilityTheory.IsGaussian (MeasureTheory.Measure.map X P)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 196 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.Measure.mapstatement · cited by 858
- ProbabilityTheory.HasGaussianLawstatement and proof · cited by 67
- ProbabilityTheory.IsGaussianstatement · cited by 48
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
- ProbabilityTheory.HasGaussianLaw.map_of_measurableproof · cited by 4
- ProbabilityTheory.HasGaussianLaw.map_eq_gaussianRealproof · cited by 2
- ProbabilityTheory.HasGaussianLaw.congrproof · cited by 1
- ProbabilityTheory.IsGaussianProcess.congrproof · cited by 0