Theorems · Theorem · probability

ProbabilityTheory.IsGaussian.hasGaussianLaw_id

∀ {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommMonoid E] [inst_2 : Module ℝ E] {mE : MeasurableSpace E}
  {μ : MeasureTheory.Measure E} [ProbabilityTheory.IsGaussian μ], ProbabilityTheory.HasGaussianLaw id μ

Defined in: Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace AddCommMonoid Module ProbabilityTheory.IsGaussian

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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
ProbabilityTheory.HasGaussianLawstatement · cited by 67
ProbabilityTheory.IsGaussianstatement and proof · cited by 48
MeasureTheory.Measure.map_idproof · cited by 29

Cited by3

Results whose statement or proof uses this declaration.

ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
ProbabilityTheory.BrownianReal.measurePreserving_eval_projectiveFamilyproof · cited by 1
ProbabilityTheory.BrownianReal.measurePreserving_eval_sub_eval_projectiveFamilyproof · cited by 1