`BookProof.OdeUnitaryFlow.lintegral_comp_invMap` (g : ℝ → ℝ≥0∞) : ∫⁻ x, ENNReal.ofReal ((x ^ 2)⁻¹) * g (invMap x) = ∫⁻ y, g y

Proved

BookProof.OdeUnitaryFlow.lintegral_comp_invMap

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

BookProof.OdeUnitaryFlow.lintegral_comp_invMap (g : ℝ → ℝ≥0∞) : ∫⁻ x, ENNReal.ofReal ((x ^ 2)⁻¹) * g (invMap x) = ∫⁻ y, g y

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

Preamble

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



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

theorem BookProof.OdeUnitaryFlow.lintegral_comp_invMap (g : ℝ → ℝ≥0∞) :
    ∫⁻ x, ENNReal.ofReal ((x ^ 2)⁻¹) * g (invMap x) = ∫⁻ y, g y := by sorry

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