compMeasurable_mk — Mathlib

English

Composition with a measurable function in the mk form yields an a.e.-stable measurable composition.

Русский

Композиция измеримой функции в форме mk даёт AE_eq-совместимую композицию.

LaTeX

$$$\\mathrm{compMeasurable\\_mk}(g,hg,f,hf) = \\mathrm{mk}(g\\circ f)(hg\\circ hf)$$$

Lean4

@[simp]
theorem compMeasurable_mk (g : β → γ) (hg : Measurable g) (f : α → β) (hf : AEStronglyMeasurable f μ) :
    compMeasurable g hg (mk f hf : α →ₘ[μ] β) =
      mk (g ∘ f) (hg.comp_aemeasurable hf.aemeasurable).aestronglyMeasurable :=
  rfl

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