`BookProof.ChapterSphericalPlancherel.integral_eq_two_mul_of_even_real` (h : ℝ → ℝ) (he : ∀ x, h (-x) = h x) : ∫ x : ℝ, h x = 2 * ∫ x in Ioi (0 : ℝ), h x

Proved

BookProof.ChapterSphericalPlancherel.integral_eq_two_mul_of_even_real

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_mul_of_even_real (h : ℝ → ℝ) (he : ∀ x, h (-x) = h x) : ∫ x : ℝ, h x = 2 * ∫ x in Ioi (0 : ℝ), h x

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

Preamble

-- Generated from ChapterSphericalPlancherel.lean — theorem BookProof.ChapterSphericalPlancherel.integral_eq_two_mul_of_even_real
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_mul_of_even_real (h : ℝ → ℝ) (he : ∀ x, h (-x) = h x) :
    ∫ x : ℝ, h x = 2 * ∫ x in Ioi (0 : ℝ), h x := by sorry

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