`BookProof.ChapterG2.no_translation_invariant_probabilityMeasure` {G : Type*} [Group G] [Countable G] [Infinite G] [MeasurableSpace G] [MeasurableSingletonClass G] : ¬ ∃ μ : Measur

Proved

BookProof.ChapterG2.no_translation_invariant_probabilityMeasure

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG2.

BookProof.ChapterG2.no_translation_invariant_probabilityMeasure {G : Type*} [Group G] [Countable G] [Infinite G] [MeasurableSpace G] [MeasurableSingletonClass G] : ¬ ∃ μ : Measure G, IsProbabilityMeasure μ ∧ ∀ g x : G, μ {g * x} = μ {x}

Formalization note: Lean 4 identifier BookProof.ChapterG2.no_translation_invariant_probabilityMeasure.

Preamble

-- Generated from ChapterG2.lean — theorem BookProof.ChapterG2.no_translation_invariant_probabilityMeasure
import Mathlib
import Definitions.Def_ChapterG2
open BookProof.ChapterG2


open MeasureTheory ProbabilityTheory
open scoped ProbabilityTheory

variable {Ω : Type*} [MeasurableSpace Ω]

Formal statement

theorem BookProof.ChapterG2.no_translation_invariant_probabilityMeasure {G : Type*} [Group G]
    [Countable G] [Infinite G] [MeasurableSpace G] [MeasurableSingletonClass G] :
    ¬ ∃ μ : Measure G, IsProbabilityMeasure μ ∧ ∀ g x : G, μ {g * x} = μ {x} := by sorry

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