`BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn` (a : atomSet mu) : (atomVec mu a : α → ℂ) =ᵐ[mu] fun x => (((Real.sqrt (mu.real {(a : α)}))⁻¹ : ℝ) : ℂ) * Set.indicator {(a : α

Proved

BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAtomicDiagonalModel.

BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn (a : atomSet mu) : (atomVec mu a : α → ℂ) =ᵐ[mu] fun x => (((Real.sqrt (mu.real {(a : α)}))⁻¹ : ℝ) : ℂ) * Set.indicator {(a : α)} (fun _ => (1 : ℂ)) x

Formalization note: Lean 4 identifier BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn.

Preamble

-- Generated from ChapterAtomicDiagonalModel.lean — theorem BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn
import Definitions.Def_ChapterMeasureAtomicDiffuse
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterAtomicDiagonalModel
open BookProof.ChapterAtomicDiagonalModel


noncomputable section

open MeasureTheory


open BookProof.ChapterMeasureAtomicDiffuse BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] [MeasurableSingletonClass α]
  (mu : Measure α) [IsFiniteMeasure mu]

Formal statement

theorem BookProof.ChapterAtomicDiagonalModel.atomVec_coeFn (a : atomSet mu) :
    (atomVec mu a : α → ℂ) =ᵐ[mu] fun x =>
      (((Real.sqrt (mu.real {(a : α)}))⁻¹ : ℝ) : ℂ) *
        Set.indicator {(a : α)} (fun _ => (1 : ℂ)) x := by sorry

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