Doob's consistency of a non-Bayesian updating process

We consider an asymptotic property of the posterior distribution (belief) of a non-Bayesian updating process. For the Bayesian updating process, the corresponding prop-erty is known as Doob's consistency. The result of our study provides a sufficient condition for the non-Bayesian updating process to satisfy this property.(c) 2023 The Author(s). Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).