`BookProof.ChapterMixedPrior.isProbabilityMeasure_normalizedContinuousPart` (mu : Measure X) [IsFiniteMeasure mu] (h : ¬ IsPurelyAtomic mu) : IsProbabilityMeasure (normalizedContin

Proved

BookProof.ChapterMixedPrior.isProbabilityMeasure_normalizedContinuousPart

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMixedPrior.

BookProof.ChapterMixedPrior.isProbabilityMeasure_normalizedContinuousPart (mu : Measure X) [IsFiniteMeasure mu] (h : ¬ IsPurelyAtomic mu) : IsProbabilityMeasure (normalizedContinuousPart mu)

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

Preamble

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


open MeasureTheory ProbabilityTheory


open BookProof.ChapterAtomicDecomposition

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

Formal statement

theorem BookProof.ChapterMixedPrior.isProbabilityMeasure_normalizedContinuousPart (mu : Measure X)
    [IsFiniteMeasure mu] (h : ¬ IsPurelyAtomic mu) :
    IsProbabilityMeasure (normalizedContinuousPart mu) := by sorry

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