Theorems · Theorem · probability

ProbabilityTheory.condIndep_iSup_of_disjoint

∀ {Ω : Type u_1} {ι : Type u_2} {m' mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ}
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] {m : ι → MeasurableSpace Ω},
  (∀ (i : ι), m i ≤ mΩ) →
    ProbabilityTheory.iCondIndep m' hm' m μ →
      ∀ {S T : Set ι}, Disjoint S T → ProbabilityTheory.CondIndep m' (⨆ i ∈ S, m i) (⨆ i ∈ T, m i) hm' μ

Defined in

Mathlib.Probability.Independence.Conditional

Cited by

0 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

StandardBorelSpaceMeasureTheory.IsFiniteMeasure