measurable — Mathlib

English

If β is a Borel space and the underlying measurable structure is suitable, then any AEEqFun f is measurable when viewed via its cast.

Русский

Если β есть пространство Бореля и соответствующая структура измеримости, то любая AEEqFun f измерима через приведение.

LaTeX

$$theorem measurable [PseudoMetrizableSpace β] [MeasurableSpace β] [BorelSpace β] (f : MeasureTheory.AEEqFun α β μ) : Measurable f.cast$$

Lean4

@[fun_prop]
protected theorem measurable [PseudoMetrizableSpace β] [MeasurableSpace β] [BorelSpace β] (f : α →ₘ[μ] β) :
    Measurable f :=
  f.stronglyMeasurable.measurable

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