`BookProof.ChapterMackeyQuasiInvariant.dens_eq_one_of_invariant` {μ : Measure X} [SigmaFinite μ] (hinv : ∀ g : G, (μ.map fun x : X => g • x) = μ) (g : G) : dens μ g =ᵐ[μ] fun _ =>

Proved

BookProof.ChapterMackeyQuasiInvariant.dens_eq_one_of_invariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMackeyQuasiInvariant.

BookProof.ChapterMackeyQuasiInvariant.dens_eq_one_of_invariant {μ : Measure X} [SigmaFinite μ] (hinv : ∀ g : G, (μ.map fun x : X => g • x) = μ) (g : G) : dens μ g =ᵐ[μ] fun _ => 1

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

Preamble

-- Generated from ChapterMackeyQuasiInvariant.lean — theorem BookProof.ChapterMackeyQuasiInvariant.dens_eq_one_of_invariant
import Mathlib
import Definitions.Def_ChapterMackeyQuasiInvariant
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.dens_eq_one_of_invariant {μ : Measure X} [SigmaFinite μ]
    (hinv : ∀ g : G, (μ.map fun x : X => g • x) = μ) (g : G) :
    dens μ g =ᵐ[μ] fun _ => 1 := by sorry

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