We construct a rank one infinite measure preserving transformation T such that for all sequences of nonzero integers {k1,...,kr}, Tk1×...×Tkr is ergodic.
@article{arxiv.math/9803105,
title = {Power Weakly Mixing Infinite Transformations},
author = {Sarah L. Day and Brian R. Grivna and Earle P. McCartney and Cesar E. Silva},
journal= {arXiv preprint arXiv:math/9803105},
year = {2007}
}