Theorems · Theorem · probability

ProbabilityTheory.HasGaussianLaw.map_fun

∀ {Ω : Type u_1} {E : Type u_2} {F : Type u_3} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω}
  [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] [BorelSpace E] {X : Ω → E} [inst_3 : NormedSpace ℝ E]
  [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace ℝ F] [inst_6 : MeasurableSpace F] [BorelSpace F],
  ProbabilityTheory.HasGaussianLaw X P → ∀ (L : E →L[ℝ] F), ProbabilityTheory.HasGaussianLaw (fun ω => L (X ω)) P

Defined in

Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic

Cited by

1 results in Mathlib

Foundations

Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpaceBorelSpaceNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpace