Vector Valued Martingale-Ergodic and Ergodic-Martingale Theorems

TL;DR

This paper establishes new vector-valued martingale-ergodic and ergodic-martingale theorems, including inequalities and extensions to weighted and multiparameter cases, advancing the theoretical framework in ergodic theory.

Contribution

It introduces novel vector-valued martingale-ergodic and ergodic-martingale theorems with inequalities, extending to weighted and multiparameter settings.

Findings

Proved vector-valued martingale-ergodic theorems

Established dominant and maximal inequalities

Extended results to weighted and multiparameter cases

Abstract

We prove martingale-ergodic and ergodic-martingale theorems for vector valued Bochner integrable functions. We obtain dominant and maximal inequalities. We also prove weighted and multiparameter martingale-ergodic and ergodic martingale theorems.