`BookProof.ChapterLpRestrictSplit.restrictEmbed_restrictProj_coeFn` {A : Set α} (hA : MeasurableSet A) (u : Lp ℂ 2 mu) : (restrictEmbed hA (restrictProj A u) : α → ℂ) =ᵐ[mu] A.indi

Proved

BookProof.ChapterLpRestrictSplit.restrictEmbed_restrictProj_coeFn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpRestrictSplit.

BookProof.ChapterLpRestrictSplit.restrictEmbed_restrictProj_coeFn {A : Set α} (hA : MeasurableSet A) (u : Lp ℂ 2 mu) : (restrictEmbed hA (restrictProj A u) : α → ℂ) =ᵐ[mu] A.indicator (u : α → ℂ)

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

Preamble

-- Generated from ChapterLpRestrictSplit.lean — theorem BookProof.ChapterLpRestrictSplit.restrictEmbed_restrictProj_coeFn
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.restrictEmbed_restrictProj_coeFn {A : Set α} (hA : MeasurableSet A) (u : Lp ℂ 2 mu) :
    (restrictEmbed hA (restrictProj A u) : α → ℂ) =ᵐ[mu] A.indicator (u : α → ℂ) := by sorry

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