of_subtype_image — Mathlib

English

If f : α → β is measurable, then the composed function a ↦ (f a) (viewed in β) is measurable.

Русский

Если f : α → β измеримо, то композиция a ↦ (f a) в β измерима.

LaTeX

$$$\\\\operatorname{Measurable} f \\\\Rightarrow \\\\operatorname{Measurable}(\\\\lambda a \\\\:\\\\rightarrow (f a))$$$

Lean4

theorem of_subtype_image {s : Set α} {t : Set s} (h : MeasurableSet (Subtype.val '' t)) : MeasurableSet t :=
  ⟨_, h, preimage_image_eq _ Subtype.val_injective⟩

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