mk — Mathlib · SciLib

English

A simp lemma giving AEStronglyMeasurable on a union equals the conjunction of AEStronglyMeasurable on the parts.

Русский

Лемма-simp: AEStronglyMeasurable на объединении равно конъюнкции для частей.

LaTeX

$$$\text{AEStronglyMeasurable}(f, μ.restrict(s \cup t)) \iff \text{AEStronglyMeasurable}(f, μ.restrict(s)) \land \text{AEStronglyMeasurable}(f, μ.restrict(t)).$$$

Lean4

/-- A `fin_strongly_measurable` function such that `f =ᵐ[μ] hf.mk f`. See lemmas
`fin_strongly_measurable_mk` and `ae_eq_mk`. -/
protected noncomputable def mk (f : α → β) (hf : AEFinStronglyMeasurable f μ) : α → β :=
  hf.choose

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