2023/07/13 by Xiongping Dai, Dai, Xiongping, Hailan Liang +3
Economics, Econometrics and Finance · Mathematics · #37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2307.06653
openalex publication_date 2023/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Veech's Theorem claims that if G is a locally compact (LC) Hausdorff topological group, then it may act freely on G^\textrmLUC. We prove Veech's Theorem for G being only locally quasi-totally bounded, not necessarily LC. And we show that the universal a.a. flow is the maximal almost 1-1 extension of the universal minimal a.p. flow and is unique up to almost 1-1 extensions. In particular, every endomorphism of Veech's hull flow induced by an a.a. function is almost 1-1; for G=ℤ or ℝ, G acts freely on its canonical universal a.a. space. Finally, we characterize Bochner a.a. functions on a LC group G in terms of Bohr a.a. function on G (due to Veech 1965 for the special case that G is abelian, LC, σ-compact, and first countable).