Prove2Me

`BookProof.ChapterG2.no_translation_invariant_unit_vector` {G : Type*} [Group G] [Infinite G] : ¬ ∃ Ψ : lp (fun _ : G => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ g x : G, Ψ (g * x) = Ψ x

Proved
BookProof.ChapterG2.no_translation_invariant_unit_vector

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_unit_vector {G : Type*} [Group G] [Infinite G] : ¬ ∃ Ψ : lp (fun _ : G => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ g x : G, Ψ (g * x) = Ψ x

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

Preamble
-- Generated from ChapterG2.lean — theorem BookProof.ChapterG2.no_translation_invariant_unit_vector
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_unit_vector {G : Type*} [Group G] [Infinite G] :
    ¬ ∃ Ψ : lp (fun _ : G => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ g x : G, Ψ (g * x) = Ψ x := by sorry

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