measurable_of_measurable_coe — Mathlib

English

The map μ ↦ μ s is measurable for every measurable set s; i.e., the evaluation on measurable sets is a measurable map.

Русский

Картина μ ↦ μ(s) измерима для каждого измеримого множества s; то есть отображение по множеству измеримо.

LaTeX

$$$\text{measurable }(\mu \mapsto \mu(s))$ for MeasurableSet s; i.e., Measurable functor.$$

Lean4

theorem measurable_of_measurable_coe (f : β → Measure α)
    (h : ∀ (s : Set α), MeasurableSet s → Measurable fun b => f b s) : Measurable f :=
  Measurable.of_le_map <|
    iSup₂_le fun s hs => MeasurableSpace.comap_le_iff_le_map.2 <| by rw [MeasurableSpace.map_comp]; exact h s hs

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