`BookProof.ChapterLpScaleMeasure.scaleUnitary_intertwines` (hc0 : c ≠ 0) (hctop : c ≠ ⊤) {g : α → ℂ} (hg : MemLp g ⊤ (c • nu)) (u : Lp ℂ 2 (c • nu)) : (scaleUnitary hc0 hctop (mult

Proved

BookProof.ChapterLpScaleMeasure.scaleUnitary_intertwines

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpScaleMeasure.

BookProof.ChapterLpScaleMeasure.scaleUnitary_intertwines (hc0 : c ≠ 0) (hctop : c ≠ ⊤) {g : α → ℂ} (hg : MemLp g ⊤ (c • nu)) (u : Lp ℂ 2 (c • nu)) : (scaleUnitary hc0 hctop (multOp g hg u) : α → ℂ) =ᵐ[nu] fun x => g x * (scaleUnitary (nu := nu) hc0 hctop u : α → ℂ) x

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

Preamble

-- Generated from ChapterLpScaleMeasure.lean — theorem BookProof.ChapterLpScaleMeasure.scaleUnitary_intertwines
import Mathlib
import Definitions.Def_ChapterLpScaleMeasure
import Definitions.Def_ChapterLinftyMultiplication
open BookProof.ChapterLinftyMultiplication
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_intertwines (hc0 : c ≠ 0) (hctop : c ≠ ⊤) {g : α → ℂ}
    (hg : MemLp g ⊤ (c • nu)) (u : Lp ℂ 2 (c • nu)) :
    (scaleUnitary hc0 hctop (multOp g hg u) : α → ℂ)
      =ᵐ[nu] fun x => g x * (scaleUnitary (nu := nu) hc0 hctop u : α → ℂ) x := by sorry

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