Theorems · Theorem · probability

ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {m0 : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω}
  {μα : MeasureTheory.Measure α} [h : ∀ (a : α), MeasureTheory.IsFiniteMeasure (κ a)] {t : Set Ω},
  ProbabilityTheory.Kernel.IndepSet t t κ μα → ∀ᵐ (a : α) ∂μα, (κ a) t = 0 ∨ (κ a) t = 1

Defined in

Mathlib.Probability.Independence.ZeroOne

Cited by

3 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasure