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Abstract
In this paper, we build the Brin-Katok's formula of conditional entropy with respect to invariant, decreasing and a large family of increasing measurable partitions by replacing the Bowen metric with the Feldman-Katok metric.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
We would like to thank Xiaomin Zhou for sharing his latest work [Citation19] with us. We also thank Jie Li for many valuable discussions. Research of Xiaona Fang is supported by Graduate Research and Practice Innovation Program of Jiangsu Province [grant number KYCX22_2777] and NNSF of China [grant number 12031019]; Ran Lu is supported by Graduate Research and Practice Innovation Program of Jiangsu Normal University [grant number 2021XKT0822].