`BookProof.OdeUnitaryFlow.chartW_lintegral_normSq` (ψ : ℝ → ℂ) : ∫⁻ x, ENNReal.ofReal (‖chartW ψ x‖ ^ 2) = ∫⁻ y, ENNReal.ofReal (‖ψ y‖ ^ 2)

Proved

BookProof.OdeUnitaryFlow.chartW_lintegral_normSq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

BookProof.OdeUnitaryFlow.chartW_lintegral_normSq (ψ : ℝ → ℂ) : ∫⁻ x, ENNReal.ofReal (‖chartW ψ x‖ ^ 2) = ∫⁻ y, ENNReal.ofReal (‖ψ y‖ ^ 2)

Formalization note: Lean 4 identifier BookProof.OdeUnitaryFlow.chartW_lintegral_normSq.

Preamble

-- Generated from ChapterOdeUnitaryFlow.lean — theorem BookProof.OdeUnitaryFlow.chartW_lintegral_normSq
import Mathlib
import Definitions.Def_ChapterOdeUnitaryFlow
open BookProof.OdeUnitaryFlow



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

theorem BookProof.OdeUnitaryFlow.chartW_lintegral_normSq (ψ : ℝ → ℂ) :
    ∫⁻ x, ENNReal.ofReal (‖chartW ψ x‖ ^ 2) = ∫⁻ y, ENNReal.ofReal (‖ψ y‖ ^ 2) := by sorry

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