`BookProof.ChapterBornMeasure.lintegral_bornDensity` (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) : ∫⁻ x, ‖(psi : α → ℂ) x‖ₑ ^ 2 ∂μ = 1

Proved

BookProof.ChapterBornMeasure.lintegral_bornDensity

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBornMeasure.

BookProof.ChapterBornMeasure.lintegral_bornDensity (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) : ∫⁻ x, ‖(psi : α → ℂ) x‖ₑ ^ 2 ∂μ = 1

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

Preamble

-- Generated from ChapterBornMeasure.lean — theorem BookProof.ChapterBornMeasure.lintegral_bornDensity
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.lintegral_bornDensity (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) :
    ∫⁻ x, ‖(psi : α → ℂ) x‖ₑ ^ 2 ∂μ = 1 := by sorry

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