`BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry` (U : Lp ℂ 2 μ ≃ₗᵢ[ℂ] Lp ℂ 2 μ) (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) : IsProbabilityMeasure...

Proved

BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBornMeasure.

BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry (U : Lp ℂ 2 μ ≃ₗᵢ[ℂ] Lp ℂ 2 μ) (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) : IsProbabilityMeasure (bornMeasure (U psi))

Formalization note: Lean 4 identifier BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry.

Preamble

-- Generated from ChapterBornMeasure.lean — theorem BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry
import Mathlib
import Definitions.Def_ChapterBornMeasure
open BookProof.ChapterBornMeasure


open MeasureTheory
open scoped ENNReal


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterBornMeasure.isProbabilityMeasure_bornMeasure_isometry (U : Lp ℂ 2 μ ≃ₗᵢ[ℂ] Lp ℂ 2 μ)
    (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) : IsProbabilityMeasure (bornMeasure (U psi)) := by sorry

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