Theorems · Theorem · probability

ProbabilityTheory.Kernel.indepSets_singleton_iff

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {s t : Set Ω} {_mΩ : MeasurableSpace Ω}
  {κ : ProbabilityTheory.Kernel α Ω} {μ : MeasureTheory.Measure α},
  ProbabilityTheory.Kernel.IndepSets {s} {t} κ μ ↔ ∀ᵐ (a : α) ∂μ, (κ a) (s ∩ t) = (κ a) s * (κ a) t

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

1 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound