`BookProof.LocalityConstraint.graphSet_gaussian_null` (m₁ m₂ : ℝ) (v₁ : ℝ≥0) (v₂ : ℝ≥0) (hv₂ : v₂ ≠ 0) {f : ℝ → ℝ} (hf : Measurable f) : ((gaussianReal m₁...

Proved

BookProof.LocalityConstraint.graphSet_gaussian_null

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLocalityConstraintNull.

BookProof.LocalityConstraint.graphSet_gaussian_null (m₁ m₂ : ℝ) (v₁ : ℝ≥0) (v₂ : ℝ≥0) (hv₂ : v₂ ≠ 0) {f : ℝ → ℝ} (hf : Measurable f) : ((gaussianReal m₁ v₁).prod (gaussianReal m₂ v₂)) (graphSet f) = 0

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

Preamble

-- Generated from ChapterLocalityConstraintNull.lean — theorem BookProof.LocalityConstraint.graphSet_gaussian_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_gaussian_null (m₁ m₂ : ℝ) (v₁ : ℝ≥0) (v₂ : ℝ≥0) (hv₂ : v₂ ≠ 0)
    {f : ℝ → ℝ} (hf : Measurable f) :
    ((gaussianReal m₁ v₁).prod (gaussianReal m₂ v₂)) (graphSet f) = 0 := by sorry

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