eval — Mathlib

English

If g is AEMeasurable on α → Π a, X a, then for each a, the map x ↦ g(x)(a) is AEMeasurable with respect to μ.

Русский

Если g AEMeasurable на α → Π a, X a, то для каждого a карта x ↦ g(x)(a) является AEMeasurable по отношению к μ.

LaTeX

$$$\mathrm{AEMeasurable}\ g\ \mu \rightarrow \forall a, \mathrm{AEMeasurable}(\lambda x. g\,x\,a)\ \mu$$$

Lean4

@[measurability]
protected theorem eval {g : α → Π a, X a} (hg : AEMeasurable g μ) (a : δ) : AEMeasurable (fun x ↦ g x a) μ :=
  by
  use fun x ↦ hg.mk g x a, hg.measurable_mk.eval
  exact hg.ae_eq_mk.mono fun _ h ↦ congrFun h _

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