`BookProof.ChapterF3.disjoint_support_inner_zero` {α : Type*} [MeasurableSpace α] (μ : MeasureTheory.Measure α) (f g : α → ℂ) (h : Disjoint (Function.support f) (Function.support g

Proved

BookProof.ChapterF3.disjoint_support_inner_zero

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF3.

BookProof.ChapterF3.disjoint_support_inner_zero {α : Type*} [MeasurableSpace α] (μ : MeasureTheory.Measure α) (f g : α → ℂ) (h : Disjoint (Function.support f) (Function.support g)) : ∫ x, (starRingEnd ℂ) (f x) * g x ∂μ = 0

Formalization note: Lean 4 identifier BookProof.ChapterF3.disjoint_support_inner_zero.

Preamble

-- Generated from ChapterF3.lean — theorem BookProof.ChapterF3.disjoint_support_inner_zero
import Mathlib
import Definitions.Def_ChapterF3
open BookProof.ChapterF3


open scoped BigOperators
open Polynomial


noncomputable section

Formal statement

theorem BookProof.ChapterF3.disjoint_support_inner_zero {α : Type*} [MeasurableSpace α] (μ : MeasureTheory.Measure α)
    (f g : α → ℂ) (h : Disjoint (Function.support f) (Function.support g)) :
    ∫ x, (starRingEnd ℂ) (f x) * g x ∂μ = 0 := by sorry

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