`BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport` {W : V → ℝ} (hW : Continuous W) (hWc : HasCompactSupport W) : MemLp (fun x => (W x : ℂ)) (⊤ : ℝ≥0∞) (volume

Proved

BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveUnboundedPotential.

BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport {W : V → ℝ} (hW : Continuous W) (hWc : HasCompactSupport W) : MemLp (fun x => (W x : ℂ)) (⊤ : ℝ≥0∞) (volume : Measure V)

Formalization note: Lean 4 identifier BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport.

Preamble

-- Generated from ChapterWaveUnboundedPotential.lean — theorem BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport
import Mathlib
import Definitions.Def_ChapterWaveUnboundedPotential
import Definitions.Def_ChapterStrichartzWave
open BookProof.StrichartzWave



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace ENNReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]

variable {ι : Type*} [Fintype ι]

Formal statement

theorem BookProof.StrichartzWave.memLp_top_of_continuous_of_hasCompactSupport {W : V → ℝ} (hW : Continuous W)
    (hWc : HasCompactSupport W) :
    MemLp (fun x => (W x : ℂ)) (⊤ : ℝ≥0∞) (volume : Measure V) := by sorry

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