Theorems · Theorem · probability

ProbabilityTheory.iCondIndepFun.condIndepFun_finsetProd_of_notMem

∀ {Ω : Type u_1} {ι : Type u_2} {β : Type u_3} {m' mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {m : MeasurableSpace β}
  [inst_2 : CommMonoid β] [MeasurableMul₂ β] {f : ι → Ω → β},
  ProbabilityTheory.iCondIndepFun m' hm' f μ →
    (∀ (i : ι), Measurable (f i)) →
      ∀ {s : Finset ι} {i : ι}, i ∉ s → ProbabilityTheory.CondIndepFun m' hm' (∏ j ∈ s, f j) (f i) μ

Defined in

Mathlib.Probability.Independence.Conditional

Cited by

1 results in Mathlib

Foundations

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

Assumes

StandardBorelSpaceMeasureTheory.IsFiniteMeasureCommMonoidMeasurableMul₂