`BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv` (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) : (stdGaussian n).map L = stdGaussian n

Proved

BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldGaussian.

BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) : (stdGaussian n).map L = stdGaussian n

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv.

Preamble

-- Generated from ChapterFreeFieldGaussian.lean — theorem BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv
import Mathlib
import Definitions.Def_ChapterFreeFieldGaussian
open BookProof.ChapterFreeFieldGaussian

variable {n : ℕ}


open MeasureTheory ProbabilityTheory Complex WithLp
open scoped RealInnerProductSpace ENNReal

Formal statement

theorem BookProof.ChapterFreeFieldGaussian.stdGaussian_map_linearIsometryEquiv
    (L : EuclideanSpace ℝ (Fin n) ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n)) :
    (stdGaussian n).map L = stdGaussian n := by sorry

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