Theorems · Theorem · probability

ProbabilityTheory.CondIndepSets.condIndep

∀ {Ω : Type u_1} {m' m₁ m₂ mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {p1 p2 : Set (Set Ω)},
  m₁ ≤ mΩ →
    m₂ ≤ mΩ →
      IsPiSystem p1 →
        IsPiSystem p2 →
          m₁ = MeasurableSpace.generateFrom p1 →
            m₂ = MeasurableSpace.generateFrom p2 →
              ProbabilityTheory.CondIndepSets m' hm' p1 p2 μ → ProbabilityTheory.CondIndep m' m₁ m₂ hm' μ

Defined in

Mathlib.Probability.Independence.Conditional

Cited by

0 results in Mathlib

Foundations

Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

StandardBorelSpaceMeasureTheory.IsFiniteMeasure