`BookProof.WeakSecondDeriv.eq_zero_out` {g : ℝ → ℝ} {R : ℝ} (hsupp : tsupport g ⊆ Icc (-R) R) {x : ℝ} (hx : x ∉ Icc (-R) R) : g x = 0

Proved

BookProof.WeakSecondDeriv.eq_zero_out

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.eq_zero_out {g : ℝ → ℝ} {R : ℝ} (hsupp : tsupport g ⊆ Icc (-R) R) {x : ℝ} (hx : x ∉ Icc (-R) R) : g x = 0

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

Preamble

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



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section

Formal statement

theorem BookProof.WeakSecondDeriv.eq_zero_out {g : ℝ → ℝ} {R : ℝ} (hsupp : tsupport g ⊆ Icc (-R) R)
    {x : ℝ} (hx : x ∉ Icc (-R) R) : g x = 0 := by sorry

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