`BookProof.ChapterMackeyQuasiInvariant.proj_idem` (μ : Measure X) {E : Set X} (hE : MeasurableSet E) (f : Lp K 2 μ) : proj μ hE (proj μ hE f) = proj μ hE f

Proved

BookProof.ChapterMackeyQuasiInvariant.proj_idem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMackeyQuasiInvariant.

BookProof.ChapterMackeyQuasiInvariant.proj_idem (μ : Measure X) {E : Set X} (hE : MeasurableSet E) (f : Lp K 2 μ) : proj μ hE (proj μ hE f) = proj μ hE f

Formalization note: Lean 4 identifier BookProof.ChapterMackeyQuasiInvariant.proj_idem.

Preamble

-- Generated from ChapterMackeyQuasiInvariant.lean — theorem BookProof.ChapterMackeyQuasiInvariant.proj_idem
import Mathlib
import Definitions.Def_ChapterMackeyQuasiInvariant
import Definitions.Def_ChapterElectroweakFieldStrength
open BookProof.ChapterElectroweakFieldStrength
open BookProof.ChapterMackeyQuasiInvariant


open MeasureTheory Measure


variable {G X K : Type*} [Group G] [MeasurableSpace X] [MulAction G X]
variable [NormedAddCommGroup K] [InnerProductSpace ℂ K]

variable (μ : Measure X) (L : G → X → (K ≃ₗᵢ[ℂ] K))
variable {μ L}

Formal statement

theorem BookProof.ChapterMackeyQuasiInvariant.proj_idem (μ : Measure X) {E : Set X} (hE : MeasurableSet E) (f : Lp K 2 μ) :
    proj μ hE (proj μ hE f) = proj μ hE f := by sorry

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