StronglyMeasurable — Mathlib

English

Same equivalence as above, with an accompanying simplification variant.

Русский

Та же эквивалентность, дополненная упрощённой версией.

LaTeX

$$$\\text{AEFinStronglyMeasurable}(f,\\mu) \\iff \\text{AEMeasurable}(f,\\mu)$$$

Lean4

/-- A function is `StronglyMeasurable` if it is the limit of simple functions. -/
@[fun_prop]
def StronglyMeasurable [MeasurableSpace α] (f : α → β) : Prop :=
  ∃ fs : ℕ → α →ₛ β, ∀ x, Tendsto (fun n => fs n x) atTop (𝓝 (f x))

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