`BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic` (mu : Measure X) [IsProbabilityMeasure mu] [NullSingletonClass mu] : ¬ IsPurelyAtomic mu

Proved

BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMixedPrior.

BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic (mu : Measure X) [IsProbabilityMeasure mu] [NullSingletonClass mu] : ¬ IsPurelyAtomic mu

Formalization note: Lean 4 identifier BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic.

Preamble

-- Generated from ChapterMixedPrior.lean — theorem BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic
import Definitions.Def_ChapterAtomicDecomposition
import Mathlib
import Definitions.Def_ChapterMixedPrior
open BookProof.ChapterMixedPrior


open MeasureTheory ProbabilityTheory


open BookProof.ChapterAtomicDecomposition

variable {X : Type*} [MeasurableSpace X] [MeasurableSingletonClass X]

Formal statement

theorem BookProof.ChapterMixedPrior.atomless_prior_not_purelyAtomic (mu : Measure X) [IsProbabilityMeasure mu]
    [NullSingletonClass mu] : ¬ IsPurelyAtomic mu := by sorry

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