`BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary` : ∃ _W : Lp ℂ 2 (volume.restrict (Set.Ioi (0 : ℝ))) ≃ₗᵢ[ℂ] Lp ℂ 2 qgSrcMeasure, True

Proved

BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityHalfDensity.

BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary : ∃ _W : Lp ℂ 2 (volume.restrict (Set.Ioi (0 : ℝ))) ≃ₗᵢ[ℂ] Lp ℂ 2 qgSrcMeasure, True

Formalization note: Lean 4 identifier BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary.

Preamble

-- Generated from ChapterQuantumGravityHalfDensity.lean — theorem BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary
import Mathlib
import Definitions.Def_ChapterQuantumGravityHalfDensity
open BookProof.QuantumGravityHalfDensity



open MeasureTheory Set Filter
open scoped ENNReal

Formal statement

theorem BookProof.QuantumGravityHalfDensity.exists_halfDensity_unitary :
    ∃ _W : Lp ℂ 2 (volume.restrict (Set.Ioi (0 : ℝ))) ≃ₗᵢ[ℂ] Lp ℂ 2 qgSrcMeasure, True := by sorry

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