Theorems · Theorem · probability

ProbabilityTheory.iIndepFun.indepFun_finsetProd_of_notMem

∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {β : Type u_10}
  {m : MeasurableSpace β} [inst : CommMonoid β] [MeasurableMul₂ β] {f : ι → Ω → β},
  ProbabilityTheory.iIndepFun f μ →
    (∀ (i : ι), Measurable (f i)) → ∀ {s : Finset ι} {i : ι}, i ∉ s → ProbabilityTheory.IndepFun (∏ j ∈ s, f j) (f i) μ

Defined in

Mathlib.Probability.Independence.Basic

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidMeasurableMul₂