prod — Mathlib

English

For probability measures μ on α and ν on β, the swap map yields (μ.prod ν).map Prod.swap = ν.prod μ.

Русский

Для вероятностных мер μ и ν перестановка факторов даёт (μ.prod ν).map Prod.swap = ν.prod μ.

LaTeX

$$$ (\mu \mathrm{prod} \nu).\mathrm{map} \mathrm{Prod.swap} = \nu \mathrm{prod} \mu $$$

Lean4

/-- The binary product of probability measures. -/
noncomputable def prod (μ : ProbabilityMeasure α) (ν : ProbabilityMeasure β) : ProbabilityMeasure (α × β) :=
  ⟨μ.toMeasure.prod ν.toMeasure, by infer_instance⟩

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