measurable_bind — Mathlib

English

For the same setup as above, the range of the piecewise function is exactly {x, y}.

Русский

В той же постановке диапазон функции piecewise равен ровно {x, y}.

LaTeX

$$$$ \\mathrm{range}\\big(\\text{piecewise}(s, hs, \\mathbf{const}(x), \\mathbf{const}(y))) \\;=\\; \\{x, y\\}. $$$$

Lean4

theorem measurable_bind [MeasurableSpace γ] (f : α →ₛ β) (g : β → α → γ) (hg : ∀ b, Measurable (g b)) :
    Measurable fun a => g (f a) a := fun s hs => f.measurableSet_cut (fun a b => g b a ∈ s) fun b => hg b hs

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