`BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol` (t : ℝ) (f : X → ℂ) (p : ℝ≥0∞) : eLpNorm (evol E t f) p μ = eLpNorm f p μ

Proved

BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEnergyBoundedEvolution.

BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol (t : ℝ) (f : X → ℂ) (p : ℝ≥0∞) : eLpNorm (evol E t f) p μ = eLpNorm f p μ

Formalization note: Lean 4 identifier BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol.

Preamble

-- Generated from ChapterEnergyBoundedEvolution.lean — theorem BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol
import Definitions.Def_ChapterEnergyBandDecomposition
import Mathlib
import Definitions.Def_ChapterEnergyBoundedEvolution
open BookProof.ChapterEnergyBoundedEvolution



open MeasureTheory Complex
open scoped ENNReal
open BookProof.EnergyBandDecomposition

variable {X : Type*} [MeasurableSpace X] {μ : Measure X} {E : X → ℝ} {f : X → ℂ}

Formal statement

theorem BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol (t : ℝ) (f : X → ℂ) (p : ℝ≥0∞) :
    eLpNorm (evol E t f) p μ = eLpNorm f p μ := by sorry

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