Theorems · Theorem · probability

ProbabilityTheory.HasGaussianLaw.map_of_measurable

∀ {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} {F : Type u_5}
  [inst_3 : TopologicalSpace F] [inst_4 : AddCommMonoid F] [inst_5 : Module ℝ F] [inst_6 : MeasurableSpace F]
  [OpensMeasurableSpace F] (L : E →L[ℝ] F),
  ProbabilityTheory.HasGaussianLaw X P → Measurable ⇑L → ProbabilityTheory.HasGaussianLaw (⇑L ∘ X) P

Defined in

Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic

Cited by

4 results in Mathlib

Foundations

Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommMonoidModuleMeasurableSpaceTopologicalSpaceAddCommMonoidModuleMeasurableSpaceOpensMeasurableSpace