`BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet` (μ : Measure α) (ν : Measure ℝ) [SFinite ν] [NullSingletonClass ν] {f : α → ℝ} (hf : Measurable f) : ¬ IsP

Proved

BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLocalityConstraintNull.

BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet (μ : Measure α) (ν : Measure ℝ) [SFinite ν] [NullSingletonClass ν] {f : α → ℝ} (hf : Measurable f) : ¬ IsProbabilityMeasure ((μ.prod ν).restrict (graphSet f))

Formalization note: Lean 4 identifier BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet.

Preamble

-- Generated from ChapterLocalityConstraintNull.lean — theorem BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet
import Mathlib
import Definitions.Def_ChapterLocalityConstraintNull
open BookProof.LocalityConstraint



open MeasureTheory ProbabilityTheory
open scoped NNReal

variable {α : Type*} [MeasurableSpace α]

Formal statement

theorem BookProof.LocalityConstraint.not_isProbabilityMeasure_restrict_graphSet (μ : Measure α) (ν : Measure ℝ)
    [SFinite ν] [NullSingletonClass ν] {f : α → ℝ} (hf : Measurable f) :
    ¬ IsProbabilityMeasure ((μ.prod ν).restrict (graphSet f)) := by sorry

View graph