Exhaustive Weakly Wandering Sequences and Alpha-type Transformations

Abstract

An increasing sequence of integers, $\mathbb{B}$, is given for which there exists a family of ergodic, infinite measure preserving transformations $T_\alpha$, $0 \leq \alpha \leq 1$ so that (1) $T_\alpha$ is of $\alpha$-type and (2) $\mathbb{B}$ is an exhaustive weakly wandering sequence for each $T_\alpha$.