`BookProof.ChapterAbelianGelfandModel.oneVec_coeFn` [IsFiniteMeasure mu] : (oneVec mu : X → ℂ) =ᵐ[mu] fun _ => (1 : ℂ)

Proved

BookProof.ChapterAbelianGelfandModel.oneVec_coeFn

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianGelfandModel.

BookProof.ChapterAbelianGelfandModel.oneVec_coeFn [IsFiniteMeasure mu] : (oneVec mu : X → ℂ) =ᵐ[mu] fun _ => (1 : ℂ)

Formalization note: Lean 4 identifier BookProof.ChapterAbelianGelfandModel.oneVec_coeFn.

Preamble

-- Generated from ChapterAbelianGelfandModel.lean — theorem BookProof.ChapterAbelianGelfandModel.oneVec_coeFn
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterAbelianGelfandModel
open BookProof.ChapterAbelianGelfandModel


open MeasureTheory Complex WeakDual CompactlySupported CompactlySupportedContinuousMap
open scoped ComplexOrder


open BookProof.ChapterLinftyMultiplication

variable {X : Type*} [TopologicalSpace X] [CompactSpace X] [T2Space X]
  [MeasurableSpace X] [BorelSpace X]
variable {X : Type*} [TopologicalSpace X]
variable {X : Type*} [TopologicalSpace X] [CompactSpace X] [T2Space X]
  [MeasurableSpace X] [BorelSpace X]
  (psi : C(X, ℂ) →ₗ[ℂ] ℂ) (hpos : ∀ g : C(X, ℂ), 0 ≤ psi (star g * g))
variable {X : Type*} [MeasurableSpace X] (mu : Measure X)

Formal statement

theorem BookProof.ChapterAbelianGelfandModel.oneVec_coeFn [IsFiniteMeasure mu] : (oneVec mu : X → ℂ) =ᵐ[mu] fun _ => (1 : ℂ) := by sorry

View graph