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`BookProof.WeakSecondDeriv.integrable_test_smul` {φ : ℝ → ℝ} (hφ : IsTestFun φ) {r : ℝ → F} (hr : LocallyIntegrable r volume) : Integrable (fun x => φ x • r x) volume

Proved
BookProof.WeakSecondDeriv.integrable_test_smul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.integrable_test_smul {φ : ℝ → ℝ} (hφ : IsTestFun φ) {r : ℝ → F} (hr : LocallyIntegrable r volume) : Integrable (fun x => φ x • r x) volume

Formalization note: Lean 4 identifier BookProof.WeakSecondDeriv.integrable_test_smul.

Preamble
-- Generated from ChapterWeakSecondDerivative.lean — theorem BookProof.WeakSecondDeriv.integrable_test_smul
import Mathlib
import Definitions.Def_ChapterWeakSecondDerivative
open BookProof.WeakSecondDeriv



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section

variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F]
Formal statement
theorem BookProof.WeakSecondDeriv.integrable_test_smul {φ : ℝ → ℝ} (hφ : IsTestFun φ) {r : ℝ → F}
    (hr : LocallyIntegrable r volume) : Integrable (fun x => φ x • r x) volume := by sorry

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