Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.hasGaussianLaw

∀ {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.IsGaussian (MeasureTheory.Measure.map X P)], ProbabilityTheory.HasGaussianLaw X P

Defined in: Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace AddCommMonoid Module MeasurableSpace ProbabilityTheory.IsGaussian

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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 and proof · cited by 858
ProbabilityTheory.HasGaussianLawstatement · cited by 67
ProbabilityTheory.IsGaussianstatement and proof · cited by 48

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