`BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn` (hc0 : c ≠ 0) (hctop : c ≠ ⊤) (u : Lp ℂ 2 (c • nu)) : (scaleUnitary hc0 hctop u : α → ℂ) =ᵐ[nu] fun x => (scaleConst c : ℂ) * (

Proved

BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpScaleMeasure.

BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn (hc0 : c ≠ 0) (hctop : c ≠ ⊤) (u : Lp ℂ 2 (c • nu)) : (scaleUnitary hc0 hctop u : α → ℂ) =ᵐ[nu] fun x => (scaleConst c : ℂ) * (u : α → ℂ) x

Formalization note: Lean 4 identifier BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn.

Preamble

-- Generated from ChapterLpScaleMeasure.lean — theorem BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterLpScaleMeasure
open BookProof.ChapterLpScaleMeasure


noncomputable section

open MeasureTheory ENNReal


open BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] {nu : Measure α} {c : ENNReal}

Formal statement

theorem BookProof.ChapterLpScaleMeasure.scaleUnitary_coeFn (hc0 : c ≠ 0) (hctop : c ≠ ⊤) (u : Lp ℂ 2 (c • nu)) :
    (scaleUnitary hc0 hctop u : α → ℂ)
      =ᵐ[nu] fun x => (scaleConst c : ℂ) * (u : α → ℂ) x := by sorry

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