Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetProd_of_notMem

∀ {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 : Type u_8} {m : MeasurableSpace β}
  [inst : CommMonoid β] [MeasurableMul₂ β] {f : ι → Ω → β},
  ProbabilityTheory.Kernel.iIndepFun f κ μ →
    (∀ (i : ι), Measurable (f i)) →
      ∀ {s : Finset ι} {i : ι}, i ∉ s → ProbabilityTheory.Kernel.IndepFun (∏ j ∈ s, f j) (f i) κ μ

Defined in

Mathlib.Probability.Independence.Kernel.IndepFun

Cited by

5 results in Mathlib

Foundations

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

Assumes

CommMonoidMeasurableMul₂