aestronglyMeasurable — Mathlib

English

A continuous function from α to β is AEStronglyMeasurable when α or β has a second-countable topology (or related condition).

Русский

Непрерывная функция из α в β является AE‑строго измеримой при наличии второго счётного базиса на одной из пространств.

LaTeX

$$$\\text{Continuous}(f) \\Rightarrow AEStronglyMeasurable(f, \\mu)$ under second-countable condition$$

Lean4

/-- A continuous function from `α` to `β` is ae strongly measurable when one of the two spaces is
second countable. -/
@[fun_prop]
theorem _root_.Continuous.aestronglyMeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [PseudoMetrizableSpace β]
    [SecondCountableTopologyEither α β] (hf : Continuous f) : AEStronglyMeasurable f μ :=
  hf.stronglyMeasurable.aestronglyMeasurable

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