aemeasurable — Mathlib

English

There is a canonical AEMeasurable realization of AEStronglyMeasurable f μ, namely a measurable version that agrees μ-almost everywhere with f.

Русский

Существует каноническое AEMеасurable представление AEStronglyMeasurable f μ, совпадающее с f почти повсюду.

LaTeX

$$$\\text{AEMeasurable}(f, \\mu) = \exists g\\; (\\text{AEStronglyMeasurable}(g, \\mu) \\land f =^\\mu g)$$$

Lean4

@[fun_prop, aesop 5% apply (rule_sets := [Measurable])]
protected theorem aemeasurable {β} [MeasurableSpace β] [TopologicalSpace β] [PseudoMetrizableSpace β] [BorelSpace β]
    {f : α → β} (hf : AEStronglyMeasurable f μ) : AEMeasurable f μ :=
  ⟨hf.mk f, hf.stronglyMeasurable_mk.measurable, hf.ae_eq_mk⟩

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