Journal of the
Korean Mathematical Society
JKMS

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

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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.

Birkhoff's ergodic theorems in terms of weighted inductive means

Byoung Jin Choi, Jae Hun Kim

Jeju National University; Chungbuk National University

Abstract

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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