Theorems · Theorem · probability

ProbabilityTheory.CondIndepFun.comp

∀ {Ω : Type u_1} {β : Type u_3} {β' : Type u_4} {m' mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω]
  {hm' : m' ≤ mΩ} {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {f : Ω → β} {g : Ω → β'}
  {γ : Type u_5} {γ' : Type u_6} {_mβ : MeasurableSpace β} {_mβ' : MeasurableSpace β'} {_mγ : MeasurableSpace γ}
  {_mγ' : MeasurableSpace γ'} {φ : β → γ} {ψ : β' → γ'},
  ProbabilityTheory.CondIndepFun m' hm' f g μ →
    Measurable φ → Measurable ψ → ProbabilityTheory.CondIndepFun m' hm' (φ ∘ f) (ψ ∘ g) μ

Defined in

Mathlib.Probability.Independence.Conditional

Cited by

2 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

StandardBorelSpaceMeasureTheory.IsFiniteMeasure