Prove2Me

`BookProof.LocalityConstraint.graphSet_volume_null` {f : ℝ → ℝ} (hf : Measurable f) : (volume : Measure (ℝ × ℝ)) (graphSet f) = 0

Proved
BookProof.LocalityConstraint.graphSet_volume_null

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLocalityConstraintNull.

BookProof.LocalityConstraint.graphSet_volume_null {f : ℝ → ℝ} (hf : Measurable f) : (volume : Measure (ℝ × ℝ)) (graphSet f) = 0

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

Preamble
-- Generated from ChapterLocalityConstraintNull.lean — theorem BookProof.LocalityConstraint.graphSet_volume_null
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.graphSet_volume_null {f : ℝ → ℝ} (hf : Measurable f) :
    (volume : Measure (ℝ × ℝ)) (graphSet f) = 0 := by sorry

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