`BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy` {X : Type*} [MeasurableSpace X] [MeasurableSingletonClass X] (mu : Measure X) [IsProbabilityMeasure mu]

Proved

BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianAtomicCondensation.

BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy {X : Type*} [MeasurableSpace X] [MeasurableSingletonClass X] (mu : Measure X) [IsProbabilityMeasure mu] : (∃ n : ℕ, Nonempty (atoms mu ≃ Fin n)) ∨ Nonempty (atoms mu ≃ ℕ)

Formalization note: Lean 4 identifier BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy.

Preamble

-- Generated from ChapterAbelianAtomicCondensation.lean — theorem BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy
import Definitions.Def_ChapterAbelianDiagonalCountable
import Mathlib
import Definitions.Def_ChapterAbelianAtomicCondensation
import Definitions.Def_ChapterAtomicDecomposition
open BookProof.ChapterAtomicDecomposition
open BookProof.ChapterAbelianAtomicCondensation


open scoped ENNReal

noncomputable section


open BookProof.ChapterAbelianDiagonalCountable
open MeasureTheory

Formal statement

theorem BookProof.ChapterAbelianAtomicCondensation.atomic_measure_index_dichotomy {X : Type*} [MeasurableSpace X]
    [MeasurableSingletonClass X] (mu : Measure X) [IsProbabilityMeasure mu] :
    (∃ n : ℕ, Nonempty (atoms mu ≃ Fin n)) ∨ Nonempty (atoms mu ≃ ℕ) := by sorry

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