`BookProof.WeakSecondDeriv.absolutelyContinuous_primitive` {G : ℝ → ℝ} (hG : LocallyIntegrable G volume) {a b c : ℝ} (hc : c ∈ uIcc a b) : AbsolutelyContinuousOnInterval (fun x =>

Proved

BookProof.WeakSecondDeriv.absolutelyContinuous_primitive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.absolutelyContinuous_primitive {G : ℝ → ℝ} (hG : LocallyIntegrable G volume) {a b c : ℝ} (hc : c ∈ uIcc a b) : AbsolutelyContinuousOnInterval (fun x => ∫ t in c..x, G t) a b

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

Preamble

-- Generated from ChapterWeakSecondDerivative.lean — theorem BookProof.WeakSecondDeriv.absolutelyContinuous_primitive
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_primitive {G : ℝ → ℝ} (hG : LocallyIntegrable G volume)
    {a b c : ℝ} (hc : c ∈ uIcc a b) :
    AbsolutelyContinuousOnInterval (fun x => ∫ t in c..x, G t) a b := by sorry

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