Theorems · Theorem · probability

ProbabilityTheory.iCondIndepSets.piiUnionInter_of_notMem

∀ {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] {π : ι → Set (Set Ω)} {a : ι} {S : Finset ι},
  ProbabilityTheory.iCondIndepSets m' hm' π μ →
    a ∉ S → ProbabilityTheory.CondIndepSets m' hm' (piiUnionInter π ↑S) (π a) 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