Theorems · Theorem · probability

ProbabilityTheory.Kernel.indep_iSup_of_directed_le

∀ {α : Type u_1} {ι : Type u_3} {_mα : MeasurableSpace α} {Ω : Type u_4} {m : ι → MeasurableSpace Ω}
  {m' m0 : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α}
  [ProbabilityTheory.IsZeroOrMarkovKernel κ],
  (∀ (i : ι), ProbabilityTheory.Kernel.Indep (m i) m' κ μ) →
    (∀ (i : ι), m i ≤ m0) →
      m' ≤ m0 → Directed (fun x1 x2 => x1 ≤ x2) m → ProbabilityTheory.Kernel.Indep (⨆ i, m i) m' κ μ

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

5 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsZeroOrMarkovKernel