`BookProof.StrichartzWave.mulL2_coeFn` (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure V)) (u : Lp ℂ 2 (volume : Measure V)) : (mulL2 W u : V → ℂ) =ᵐ[(volume : Measure V)] fun x => (W x) *

Proved

BookProof.StrichartzWave.mulL2_coeFn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveBoundedPotential.

BookProof.StrichartzWave.mulL2_coeFn (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure V)) (u : Lp ℂ 2 (volume : Measure V)) : (mulL2 W u : V → ℂ) =ᵐ[(volume : Measure V)] fun x => (W x) * (u x)

Formalization note: Lean 4 identifier BookProof.StrichartzWave.mulL2_coeFn.

Preamble

-- Generated from ChapterWaveBoundedPotential.lean — theorem BookProof.StrichartzWave.mulL2_coeFn
import Mathlib
import Definitions.Def_ChapterWaveBoundedPotential
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]

Formal statement

theorem BookProof.StrichartzWave.mulL2_coeFn (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure V))
    (u : Lp ℂ 2 (volume : Measure V)) :
    (mulL2 W u : V → ℂ) =ᵐ[(volume : Measure V)] fun x => (W x) * (u x) := by sorry

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