Exhaustive weakly wandering sequences

A sequence of integers {ni : i = 0, 1…} is an exhaustive weakly wandering sequence for a transformation T if for some measurable set W, X=⋃∞i=0TniW(disj. We introduce a hereditary Property (H) for a sequence of integers associated with an infinite ergodic transformation T, and show that it is a sufficient condition for the sequence to be an exhaustive weakly wandering sequence for T. We then show that every infinite ergodic transformation admits sequences that possess Property (H), and observe that Property (H) is inherited by all subsequences of a sequence that possess it. As a corollary, we obtain an application to tiling the set of integers ℤ with infinite subsets.