compProd — Mathlib

English

Definition of compProd: a construction giving a kernel α → β×γ from kernels κ: α → β and η: β → γ, representing the joint distribution of a pair (b,c) with kernel κ and η.

Русский

Определение compProd: конструирование ядра α → β×γ из ядер κ: α → β и η: β → γ, задающее совместное распределение пары (b,c).

LaTeX

$$compProd : Kernel α β → Kernel (Prod α β) γ → Kernel α (Prod β γ)$$

Lean4

/-- Composition-Product of kernels. For s-finite kernels, it satisfies
`∫⁻ bc, f bc ∂(compProd κ η a) = ∫⁻ b, ∫⁻ c, f (b, c) ∂(η (a, b)) ∂(κ a)`
(see `ProbabilityTheory.Kernel.lintegral_compProd`).
If either of the kernels is not s-finite, `compProd` is given the junk value 0. -/
noncomputable def compProd :=
  val_proj @wrapped✝.{}

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