`BookProof.DampedOscillatorEnergy.total_probability_conserved` {Ω : Type*} [MeasurableSpace Ω] (μ : Measure Ω) [IsProbabilityMeasure μ] {T : Ω → Ω} (hT : Measurable T) : (μ.map T)

Proved

BookProof.DampedOscillatorEnergy.total_probability_conserved

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDampedOscillatorEnergy.

BookProof.DampedOscillatorEnergy.total_probability_conserved {Ω : Type*} [MeasurableSpace Ω] (μ : Measure Ω) [IsProbabilityMeasure μ] {T : Ω → Ω} (hT : Measurable T) : (μ.map T) Set.univ = 1

Formalization note: Lean 4 identifier BookProof.DampedOscillatorEnergy.total_probability_conserved.

Preamble

-- Generated from ChapterDampedOscillatorEnergy.lean — theorem BookProof.DampedOscillatorEnergy.total_probability_conserved
import Mathlib
import Definitions.Def_ChapterDampedOscillatorEnergy
open BookProof.DampedOscillatorEnergy



open MeasureTheory

Formal statement

theorem BookProof.DampedOscillatorEnergy.total_probability_conserved {Ω : Type*} [MeasurableSpace Ω] (μ : Measure Ω)
    [IsProbabilityMeasure μ] {T : Ω → Ω} (hT : Measurable T) :
    (μ.map T) Set.univ = 1 := by sorry

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