`BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed` {A : Set α} (hA : MeasurableSet A) : OrthogonalFamily ℂ (fun b : Bool => Lp ℂ 2 (mu.restrict (splitSet A b))) (splitE

Proved

BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpRestrictSplit.

BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed {A : Set α} (hA : MeasurableSet A) : OrthogonalFamily ℂ (fun b : Bool => Lp ℂ 2 (mu.restrict (splitSet A b))) (splitEmbed hA)

Formalization note: Lean 4 identifier BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed.

Preamble

-- Generated from ChapterLpRestrictSplit.lean — theorem BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterLpRestrictSplit
open BookProof.ChapterLpRestrictSplit


noncomputable section

open MeasureTheory


open BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] {mu : Measure α}

Formal statement

theorem BookProof.ChapterLpRestrictSplit.orthogonalFamily_splitEmbed {A : Set α} (hA : MeasurableSet A) :
    OrthogonalFamily ℂ (fun b : Bool => Lp ℂ 2 (mu.restrict (splitSet A b)))
      (splitEmbed hA) := by sorry

View graph