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

Proved

BookProof.OdeUnitaryFlow.lintegral_comp_mob

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

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

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

Preamble

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



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

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

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