Theorems · Theorem · probability

ProbabilityTheory.Kernel.indep_iff_forall_indepSet

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} (m₁ m₂ : MeasurableSpace Ω) {_m0 : MeasurableSpace Ω}
  (κ : ProbabilityTheory.Kernel α Ω) (μ : MeasureTheory.Measure α),
  ProbabilityTheory.Kernel.Indep m₁ m₂ κ μ ↔
    ∀ (s t : Set Ω), MeasurableSet s → MeasurableSet t → ProbabilityTheory.Kernel.IndepSet s t κ μ

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound