Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepSet_iff_meas_biInter

∀ {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} {f : ι → Set Ω},
  (∀ (i : ι), MeasurableSet (f i)) →
    (ProbabilityTheory.Kernel.iIndepSet f κ μ ↔
      ∀ (s : Finset ι), ∀ᵐ (a : α) ∂μ, (κ a) (⋂ i ∈ s, f i) = ∏ i ∈ s, (κ a) (f i))

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

2 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound