`BookProof.LocalityConstraint.restrict_graphSet_eq_zero` (μ : Measure α) (ν : Measure ℝ) [SFinite ν] [NullSingletonClass ν] {f : α → ℝ} (hf : Measurable f) : (μ.prod ν).restrict (g

Proved

BookProof.LocalityConstraint.restrict_graphSet_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLocalityConstraintNull.

BookProof.LocalityConstraint.restrict_graphSet_eq_zero (μ : Measure α) (ν : Measure ℝ) [SFinite ν] [NullSingletonClass ν] {f : α → ℝ} (hf : Measurable f) : (μ.prod ν).restrict (graphSet f) = 0

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

Preamble

-- Generated from ChapterLocalityConstraintNull.lean — theorem BookProof.LocalityConstraint.restrict_graphSet_eq_zero
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.restrict_graphSet_eq_zero (μ : Measure α) (ν : Measure ℝ) [SFinite ν] [NullSingletonClass ν]
    {f : α → ℝ} (hf : Measurable f) :
    (μ.prod ν).restrict (graphSet f) = 0 := by sorry

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