Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepSets.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} {π : ι → Set (Set Ω)},
  ProbabilityTheory.Kernel.iIndepSets π κ μ →
    ∀ (s : Finset ι) {f : ι → Set Ω}, (∀ i ∈ s, f i ∈ π i) → ∀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

3 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound