`BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even` {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] (f : ℝ → E) (h : ∀ x, f (-x) = f x) (hf : Integrable f) : ∫

Proved

BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalPlancherel.

BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] (f : ℝ → E) (h : ∀ x, f (-x) = f x) (hf : Integrable f) : ∫ x : ℝ, f x = (2 : ℝ) • ∫ x in Ioi (0 : ℝ), f x

Formalization note: Lean 4 identifier BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even.

Preamble

-- Generated from ChapterSphericalPlancherel.lean — theorem BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even
import Definitions.Def_ChapterSphericalBessel
import Mathlib
import Definitions.Def_ChapterSphericalPlancherel
open BookProof.ChapterSphericalPlancherel



open MeasureTheory Set Real SchwartzMap
open scoped FourierTransform ContDiff
open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalPlancherel.integral_eq_two_smul_of_even {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
    (f : ℝ → E) (h : ∀ x, f (-x) = f x) (hf : Integrable f) :
    ∫ x : ℝ, f x = (2 : ℝ) • ∫ x in Ioi (0 : ℝ), f x := by sorry

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