Theorems · Definition · probability

ProbabilityTheory.Kernel.iIndepSet

{α : Type u_1} →
  {Ω : Type u_2} →
    {ι : Type u_3} →
      {_mα : MeasurableSpace α} →
        {_mΩ : MeasurableSpace Ω} →
          (ι → Set Ω) →
            ProbabilityTheory.Kernel α Ω →
              autoParam (MeasureTheory.Measure α) ProbabilityTheory.Kernel.iIndepSet._auto_1 → Prop

A family of sets is independent if the family of measurable space structures they generate is independent. For a set s, the generated measurable space has measurable sets ∅, s, sᶜ, univ.

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

16 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound