Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepSets.iIndep

∀ {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) →
    ∀ (π : ι → Set (Set Ω)),
      (∀ (n : ι), IsPiSystem (π n)) →
        (∀ (i : ι), m i = MeasurableSpace.generateFrom (π i)) →
          ProbabilityTheory.Kernel.iIndepSets π κ μ → ProbabilityTheory.Kernel.iIndep m κ μ

The measurable space structures generated by independent pi-systems are independent.

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

4 results in Mathlib

Foundations

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