`BookProof.ChapterSphericalPlancherel.integral_eq_zero_of_odd` {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] (f : ℝ → E) (h : ∀ x, f (-x) = -f x) : ∫ x : ℝ, f x = 0

Proved

BookProof.ChapterSphericalPlancherel.integral_eq_zero_of_odd

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalPlancherel.

BookProof.ChapterSphericalPlancherel.integral_eq_zero_of_odd {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] (f : ℝ → E) (h : ∀ x, f (-x) = -f x) : ∫ x : ℝ, f x = 0

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

Preamble

-- Generated from ChapterSphericalPlancherel.lean — theorem BookProof.ChapterSphericalPlancherel.integral_eq_zero_of_odd
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_zero_of_odd {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
    (f : ℝ → E) (h : ∀ x, f (-x) = -f x) : ∫ x : ℝ, f x = 0 := by sorry

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