Theorems · Theorem · probability

ProbabilityTheory.iCondIndepFun.condIndepFun_prodMk_prodMk

∀ {Ω : Type u_1} {ι : Type u_2} {m' mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {β : ι → Type u_5}
  {m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
  ProbabilityTheory.iCondIndepFun m' hm' f μ →
    (∀ (i : ι), Measurable (f i)) →
      ∀ (i j k l : ι),
        i ≠ k →
          i ≠ l →
            j ≠ k → j ≠ l → ProbabilityTheory.CondIndepFun m' hm' (fun a => (f i a, f j a)) (fun a => (f k a, f l a)) μ

Defined in

Mathlib.Probability.Independence.Conditional

Cited by

0 results in Mathlib

Foundations

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

Assumes

StandardBorelSpaceMeasureTheory.IsFiniteMeasure