Theorems · Theorem · probability

ProbabilityTheory.Kernel.indep_iSup_of_disjoint

∀ {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} {m : ι → MeasurableSpace Ω},
  (∀ (i : ι), m i ≤ _mΩ) →
    ProbabilityTheory.Kernel.iIndep m κ μ →
      ∀ {S T : Set ι}, Disjoint S T → ProbabilityTheory.Kernel.Indep (⨆ i ∈ S, m i) (⨆ i ∈ T, m i) κ μ

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

3 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound