`BookProof.WeakSecondDeriv.exists_unitTest` : ∃ ρ : ℝ → ℝ, IsTestFun ρ ∧ ∫ x, ρ x = 1

Proved

BookProof.WeakSecondDeriv.exists_unitTest

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.exists_unitTest : ∃ ρ : ℝ → ℝ, IsTestFun ρ ∧ ∫ x, ρ x = 1

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

Preamble

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



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section

Formal statement

theorem BookProof.WeakSecondDeriv.exists_unitTest : ∃ ρ : ℝ → ℝ, IsTestFun ρ ∧ ∫ x, ρ x = 1 := by sorry

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