Authors: M.A. Akcoglu, J.R. Baxter, S.E. Ferrando.

Abstract: We develop a Repeated Filling Scheme for Upcrossings in the basic case, that is, in the case of the Ratio Ergodic Theorem setting. Our proof will be based on a variant of the filling scheme construction used originally by Chacon and Ornstein to prove the Maximal Ergodic Lemma. We will also strengthen Bishop's result in one direction, since we allow for a more general form of upcrossing.