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

作者：Leustean Laurentiu^*; Nicolae Adriana

来源：ARCHIV DER MATHEMATIK, 2015, 105(5): 467-477.

DOI：10.1007/s00013-015-0825-7

• Ergodic theorem
• Geodesic space
• Weak uniform convexity
• Busemann convexity

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.

• 出版日期2015-11