Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepFun.indepFun_prodMk

∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {β : ι → Type u_8}
  {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.Kernel.iIndepFun f κ μ →
    (∀ (i : ι), Measurable (f i)) →
      ∀ (i j k : ι), i ≠ k → j ≠ k → ProbabilityTheory.Kernel.IndepFun (fun a => (f i a, f j a)) (f k) κ μ

Defined in

Mathlib.Probability.Independence.Kernel.IndepFun

Cited by

7 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound