A note on an ergodic theorem in weakly uniformly convex geodesic spaces

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• 作者：Laurenţiu Leuştean ; Adriana Nicolae
• 关键词：Ergodic theorem ; Geodesic space ; Weak uniform convexity ; Busemann convexity
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：105
• 期：5
• 页码：467-477
• 全文大小：518 KB
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• 作者单位：Laurenţiu Leuştean (1) (2)
  Adriana Nicolae (3) (4)
  
  1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, P. O. Box 010014, Bucharest, Romania
  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania
  3. Department of Mathematics, Babeş-Bolyai University, Kogălniceanu 1, 400084, Cluj-Napoca, Romania
  4. Research Group of the Project PD-3-0152, Simion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

Karlsson and Margulis (Commun. Math. Phys. 208:107–123, 1999) proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that focuses on the asymptotic behavior of integrable cocycles of nonexpansive mappings over an ergodic measure-preserving transformation. In this note we show that this result holds true when assuming a weaker notion of uniform convexity.