The purpose of this paper is to present solutions to certain problems in ergodic theory suggested by Einar Hille in his book Functional analysis and semi-groups [1]. 1 Let T(t) ( > 0) be a semi-group of linear bounded transformations on a complex Banach space X to itself. Following Hille, we say that T(t) is ergodic at infinity (or at 0) if it has a generalized limit of some sort when t-*oo (or 0+). We define the Abel mean