isCaratheodory_disjointed — Mathlib

English

If all s i are Carathéodory-measurable, then disjointed s i is Carathéodory-measurable for each i.

Русский

Если все s i карatheodory-измеримы, то disjointed s i карatheodory-измерим для каждого i.

LaTeX

$$disjointed s i$$

Lean4

theorem isCaratheodory_disjointed {ι : Type*} [Preorder ι] [LocallyFiniteOrderBot ι] {s : ι → Set α}
    (h : ∀ i, m.IsCaratheodory (s i)) (i : ι) : m.IsCaratheodory (disjointed s i) :=
  disjointedRec (fun _ j ht ↦ m.isCaratheodory_diff ht <| h j) (h i)

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