`BookProof.WeakSecondDeriv.absolutelyContinuous_test` {g : ℝ → ℝ} (hg : IsTestFun g) (a b : ℝ) : AbsolutelyContinuousOnInterval g a b

Proved

BookProof.WeakSecondDeriv.absolutelyContinuous_test

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.absolutelyContinuous_test {g : ℝ → ℝ} (hg : IsTestFun g) (a b : ℝ) : AbsolutelyContinuousOnInterval g a b

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

Preamble

-- Generated from ChapterWeakSecondDerivative.lean — theorem BookProof.WeakSecondDeriv.absolutelyContinuous_test
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.absolutelyContinuous_test {g : ℝ → ℝ} (hg : IsTestFun g) (a b : ℝ) :
    AbsolutelyContinuousOnInterval g a b := by sorry

View graph