`BookProof.ChapterF7.l2pair_integrable` (f g : 𝓢(ℝ, ℂ)) : Integrable (fun x => (starRingEnd ℂ) (f x) * g x) volume

Proved

BookProof.ChapterF7.l2pair_integrable

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.l2pair_integrable (f g : 𝓢(ℝ, ℂ)) : Integrable (fun x => (starRingEnd ℂ) (f x) * g x) volume

Formalization note: Lean 4 identifier BookProof.ChapterF7.l2pair_integrable.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.l2pair_integrable
import Mathlib
import Definitions.Def_ChapterF7
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.l2pair_integrable (f g : 𝓢(ℝ, ℂ)) :
    Integrable (fun x => (starRingEnd ℂ) (f x) * g x) volume := by sorry

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