Prove2Me

`BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart` (mu : Measure X) [SFinite mu] : mu = continuousPart mu + atomicPart mu

Proved
BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAtomicDecomposition.

BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart (mu : Measure X) [SFinite mu] : mu = continuousPart mu + atomicPart mu

Formalization note: Lean 4 identifier BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart.

Preamble
-- Generated from ChapterAtomicDecomposition.lean — theorem BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart
import Mathlib
import Definitions.Def_ChapterAtomicDecomposition
open BookProof.ChapterAtomicDecomposition


open MeasureTheory


variable {X : Type*} [MeasurableSpace X] [MeasurableSingletonClass X]
Formal statement
theorem BookProof.ChapterAtomicDecomposition.eq_continuousPart_add_atomicPart (mu : Measure X) [SFinite mu] :
    mu = continuousPart mu + atomicPart mu := by sorry

View graph