`BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics` (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H) (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) (t : ℝ) : IsProbabilityMeasure

Proved

BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBornMeasure.

BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H) (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) (t : ℝ) : IsProbabilityMeasure (bornMeasure (evolve H t psi)) ∧ bornMeasure (evolve H t psi) ≪ μ

Formalization note: Lean 4 identifier BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics.

Preamble

-- Generated from ChapterBornMeasure.lean — theorem BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics
import Mathlib
import Definitions.Def_ChapterBornMeasure
open BookProof.ChapterBornMeasure


open MeasureTheory
open scoped ENNReal


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterBornMeasure.condProb_of_bounded_dynamics (H : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) (hH : IsSelfAdjoint H)
    (psi : Lp ℂ 2 μ) (hpsi : ‖psi‖ = 1) (t : ℝ) :
    IsProbabilityMeasure (bornMeasure (evolve H t psi)) ∧
      bornMeasure (evolve H t psi) ≪ μ := by sorry

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