comp₂_mk_mk — Mathlib

English

Specializing comp₂ to mk's, the result is mk of the pointwise composition g(f₁ a, f₂ a) with the appropriate measurability data.

Русский

Специализация comp₂ на mk-макеты даёт mk от покомпонентной композиции.

LaTeX

$$$comp₂\_mk\_mk(g,hg,f₁,f₂) = mk(\lambda a, g(f₁(a), f₂(a)))\ (hg.prodMk hf₂)$$$

Lean4

@[simp]
theorem comp₂_mk_mk (g : β → γ → δ) (hg : Continuous (uncurry g)) (f₁ : α → β) (f₂ : α → γ) (hf₁ hf₂) :
    comp₂ g hg (mk f₁ hf₁ : α →ₘ[μ] β) (mk f₂ hf₂) =
      mk (fun a => g (f₁ a) (f₂ a)) (hg.comp_aestronglyMeasurable (hf₁.prodMk hf₂)) :=
  rfl

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