Theorems · Theorem · probability

ProbabilityTheory.IndepFun.meas_inter

∀ {Ω : Type u_1} {β : Type u_3} {γ : Type u_4} {x : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω}
  [mβ : MeasurableSpace β] [mγ : MeasurableSpace γ] {f : Ω → β} {g : Ω → γ},
  ProbabilityTheory.IndepFun f g μ → ∀ {s t : Set Ω}, MeasurableSet s → MeasurableSet t → μ (s ∩ t) = μ s * μ t

Defined in

Mathlib.Probability.Independence.Basic

Cited by

0 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace