Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2022; 59(3): 549-570

Published online May 1, 2022

Copyright © The Korean Mathematical Society.

Birkhoff's ergodic theorems in terms of weighted inductive means

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.

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