`BookProof.ChapterBornMeasure.bornMeasure_iUnion` (psi : Lp ℂ 2 μ) {s : ℕ → Set α} (hs : ∀ n, MeasurableSet (s n)) (hd : Pairwise (Function.onFun Disjoint s)) : bornMeasure psi (⋃

Proved

BookProof.ChapterBornMeasure.bornMeasure_iUnion

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBornMeasure.

BookProof.ChapterBornMeasure.bornMeasure_iUnion (psi : Lp ℂ 2 μ) {s : ℕ → Set α} (hs : ∀ n, MeasurableSet (s n)) (hd : Pairwise (Function.onFun Disjoint s)) : bornMeasure psi (⋃ n, s n) = ∑' n, bornMeasure psi (s n)

Formalization note: Lean 4 identifier BookProof.ChapterBornMeasure.bornMeasure_iUnion.

Preamble

-- Generated from ChapterBornMeasure.lean — theorem BookProof.ChapterBornMeasure.bornMeasure_iUnion
import Mathlib
import Definitions.Def_ChapterBornMeasure
open BookProof.ChapterBornMeasure


open MeasureTheory
open scoped ENNReal


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterBornMeasure.bornMeasure_iUnion (psi : Lp ℂ 2 μ) {s : ℕ → Set α}
    (hs : ∀ n, MeasurableSet (s n)) (hd : Pairwise (Function.onFun Disjoint s)) :
    bornMeasure psi (⋃ n, s n) = ∑' n, bornMeasure psi (s n) := by sorry

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