A general local ergodic theorem in<i>L</i><sub>1</sub>
A general local ergodic theorem in<i>L</i><sub>1</sub>
Let (X,^,μ)be a σ-fίnite measure space and let L 1 denote the usual Banach space of equivalence classes of real valued integrable functions on X.We shall not distinguish between the equivalence classes and the functions themselves.Relations between functions are assumed to hold in an a.e.sense.Throughout this paper {T t } …