Theorems · Theorem · probability

ProbabilityTheory.condIndep_iSup_of_directed_le

∀ {Ω : Type u_1} {ι : Type u_2} {m' m₁ mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {m : ι → MeasurableSpace Ω},
  (∀ (i : ι), ProbabilityTheory.CondIndep m' (m i) m₁ hm' μ) →
    (∀ (i : ι), m i ≤ mΩ) →
      m₁ ≤ mΩ → Directed (fun x1 x2 => x1 ≤ x2) m → ProbabilityTheory.CondIndep m' (⨆ i, m i) m₁ 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