comp_mk — Mathlib

English

Composing a function with a continuous map respects mk: the class of g∘f is mk g∘f with the corresponding aestronglyMeasurable.

Русский

Композиция с непрерывной картой сохраняет mk-образование: класс равно mk (g∘f).

LaTeX

$$$\\mathrm{comp\\_mk}(g,hg,f,f) = \\mathrm{mk}(g \\circ f) (hg \\cdot aestronglyMeasurable)$$$

Lean4

@[simp]
theorem comp_mk (g : β → γ) (hg : Continuous g) (f : α → β) (hf) :
    comp g hg (mk f hf : α →ₘ[μ] β) = mk (g ∘ f) (hg.comp_aestronglyMeasurable hf) :=
  rfl

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