`BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one` (hn : 0 < n) : sphereGaussian n (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) = 1

Proved

BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldSphereSupport.

BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one (hn : 0 < n) : sphereGaussian n (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) = 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one.

Preamble

-- Generated from ChapterFreeFieldSphereSupport.lean — theorem BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Mathlib
import Definitions.Def_ChapterFreeFieldSphereSupport
open BookProof.ChapterFreeFieldSphereSupport

variable {n : ℕ}


open MeasureTheory ProbabilityTheory
open BookProof.ChapterFreeFieldGaussian BookProof.ChapterFreeFieldSphere

Formal statement

theorem BookProof.ChapterFreeFieldSphereSupport.sphereGaussian_sphere_eq_one (hn : 0 < n) :
    sphereGaussian n (Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1) = 1 := by sorry

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