comp₂Measurable_mk_mk — Mathlib

English

The equality of comp₂Measurable and aMK-expanded form with mk agrees; the mk form uses aemeasurable product data.

Русский

Согласуется равенство comp₂Measurable и form mk с mk-образом, используя aemeasurable-продуктовые данные.

LaTeX

$$$comp₂Measurable\ g hg f₁ f₂ =\; compMeasurable\ (Function.uncurry g) hg (f₁.pair f₂)$$$

Lean4

@[simp]
theorem comp₂Measurable_mk_mk (g : β → γ → δ) (hg : Measurable (uncurry g)) (f₁ : α → β) (f₂ : α → γ) (hf₁ hf₂) :
    comp₂Measurable g hg (mk f₁ hf₁ : α →ₘ[μ] β) (mk f₂ hf₂) =
      mk (fun a => g (f₁ a) (f₂ a))
        (hg.comp_aemeasurable (hf₁.aemeasurable.prodMk hf₂.aemeasurable)).aestronglyMeasurable :=
  rfl

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