aeStronglyMeasurable_mkD_of_uncurry

English

If f’s uncurry is continuous, then x ↦ mkD(f(x)) g is almost everywhere strongly measurable.

Русский

Если некорректирование f через uncurry непрерывно, то x ↦ mkD(f(x)) g — æ-строго измеримо.

LaTeX

$$$\text{AEStronglyMeasurable}(x \mapsto \mathrm{mkD}(f(x), g), μ).$$$

Lean4

theorem aeStronglyMeasurable_mkD_of_uncurry [CompactSpace Y] [TopologicalSpace X] [OpensMeasurableSpace X]
    [SecondCountableTopologyEither X (C(Y, E))] (f : X → Y → E) (g : C(Y, E))
    (f_cont : Continuous (Function.uncurry f)) : AEStronglyMeasurable (fun x ↦ mkD (f x) g) μ :=
  continuous_mkD_of_uncurry _ _ f_cont |>.aestronglyMeasurable

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