`BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one` (hn : 0 < n) : ((sphereGaussian n).map bornMap) (stdSimplex ℝ (Fin n)) = 1

Proved

BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBorn.

BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one (hn : 0 < n) : ((sphereGaussian n).map bornMap) (stdSimplex ℝ (Fin n)) = 1

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one.

Preamble

-- Generated from ChapterFreeFieldBorn.lean — theorem BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one
import Definitions.Def_ChapterFreeFieldGaussian
import Definitions.Def_ChapterFreeFieldSphere
import Definitions.Def_ChapterFreeFieldSphereSupport
import Mathlib
import Definitions.Def_ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBorn

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldGaussian BookProof.ChapterFreeFieldSphere
open BookProof.ChapterFreeFieldSphereSupport

Formal statement

theorem BookProof.ChapterFreeFieldBorn.bornGaussian_stdSimplex_eq_one (hn : 0 < n) :
    ((sphereGaussian n).map bornMap) (stdSimplex ℝ (Fin n)) = 1 := by sorry

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