1 Introduction and Main Results
In classical ergodic theory, one of the earliest pointwise ergodic convergence theorems was obtained by Birkhoff [1] in 1931. Dunford and Schwartz [2] greatly generalized the previous situation;they established the strong (p, p) maximal inequalities for all 1<p<∞for time averages of positive L1-L∞ contractions and obtained the pointwise convergence result as a corollary.