J. Korean Math. Soc. 2022; 59(3): 549-570
Published online May 1, 2022 https://doi.org/10.4134/JKMS.j210239
Copyright © The Korean Mathematical Society.
Byoung Jin Choi, Jae Hun Kim
Jeju National University; Chungbuk National University
In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.
Keywords: Birkhoff's ergodic theorem, weighted inductive means, barycenter, Hadamard space
MSC numbers: Primary 37A30, 28D05
Supported by: B. J. Choi was supported by the 2022 scientific promotion program funded by Jeju National University.