mass_pi — Mathlib

English

The product of probability measures is the product measure on the product space.

Русский

Произведение вероятностных мер является произведением меры на произведном пространстве.

LaTeX

$$ProbabilityMeasure.pi μ is a product measure on Π α_i: (π μ).toMeasure = Measure.pi (μ_i.toMeasure)$$

Lean4

@[simp]
theorem mass_pi : (FiniteMeasure.pi μ).mass = ∏ i, (μ i).mass :=
  by
  simp only [mass]
  rw [← pi_univ (univ : Set ι), pi_pi]

Похожие утверждения