`BookProof.ChapterG3.integral_eventProj` [MeasurableSpace X] (μ : Measure X) [IsProbabilityMeasure μ] (A : Set X) (hA : MeasurableSet A) : ∫ x, eventProj A x ∂μ = (μ A).toReal

Proved

BookProof.ChapterG3.integral_eventProj

by leonardopedro · Oct 18, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG3.

BookProof.ChapterG3.integral_eventProj [MeasurableSpace X] (μ : Measure X) [IsProbabilityMeasure μ] (A : Set X) (hA : MeasurableSet A) : ∫ x, eventProj A x ∂μ = (μ A).toReal

Formalization note: Lean 4 identifier BookProof.ChapterG3.integral_eventProj.

Preamble

-- Generated from ChapterG3.lean — theorem BookProof.ChapterG3.integral_eventProj
import Mathlib
import Definitions.Def_ChapterG3
import Definitions.Def_ChapterConservativeDiagonal
open BookProof.ConservativeDiagonal
open BookProof.ChapterG3


open MeasureTheory
open scoped ENNReal



variable {X : Type*}

Formal statement

theorem BookProof.ChapterG3.integral_eventProj [MeasurableSpace X] (μ : Measure X)
    [IsProbabilityMeasure μ] (A : Set X) (hA : MeasurableSet A) :
    ∫ x, eventProj A x ∂μ = (μ A).toReal := by sorry

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