Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepSet_iff_iIndepSets_singleton

∀ {α : Type u_1} {Ω : Type u_2} {ι : Type u_3} {_mα : MeasurableSpace α} {_mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α} {f : ι → Set Ω},
  (∀ (i : ι), MeasurableSet (f i)) →
    (ProbabilityTheory.Kernel.iIndepSet f κ μ ↔ ProbabilityTheory.Kernel.iIndepSets (fun i => {f i}) κ μ)

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

3 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound