`BookProof.ChapterSphericalPlancherel.integrable_bdd_mul` (G : ℝ → ℂ) (hG : Integrable G) (u : ℝ → ℝ) (hu : Continuous u) (hb : ∀ x, |u x| ≤ 1) : Integrable (fun x : ℝ => (u x : ℂ)

Proved

BookProof.ChapterSphericalPlancherel.integrable_bdd_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalPlancherel.

BookProof.ChapterSphericalPlancherel.integrable_bdd_mul (G : ℝ → ℂ) (hG : Integrable G) (u : ℝ → ℝ) (hu : Continuous u) (hb : ∀ x, |u x| ≤ 1) : Integrable (fun x : ℝ => (u x : ℂ) * G x)

Formalization note: Lean 4 identifier BookProof.ChapterSphericalPlancherel.integrable_bdd_mul.

Preamble

-- Generated from ChapterSphericalPlancherel.lean — theorem BookProof.ChapterSphericalPlancherel.integrable_bdd_mul
import Definitions.Def_ChapterSphericalBessel
import Mathlib
import Definitions.Def_ChapterSphericalPlancherel
open BookProof.ChapterSphericalPlancherel



open MeasureTheory Set Real SchwartzMap
open scoped FourierTransform ContDiff
open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalPlancherel.integrable_bdd_mul (G : ℝ → ℂ) (hG : Integrable G) (u : ℝ → ℝ) (hu : Continuous u)
    (hb : ∀ x, |u x| ≤ 1) : Integrable (fun x : ℝ => (u x : ℂ) * G x) := by sorry

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