Theorems · Theorem · probability

ProbabilityTheory.Kernel.deterministic_prod_deterministic

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {f : α → β} {g : α → γ} (hf : Measurable f) (hg : Measurable g),
  (ProbabilityTheory.Kernel.deterministic f hf).prod (ProbabilityTheory.Kernel.deterministic g hg) =
    ProbabilityTheory.Kernel.deterministic (fun a => (f a, g a)) ⋯

Defined in

Mathlib.Probability.Kernel.Composition.Prod

Cited by

2 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound