A rank-one infinite measure preserving flow T=(Tt)t∈R is constructed such that for each t=0, the Cartesian powers of the transformation Tt are all ergodic.
@article{arxiv.0910.2856,
title = {Rank-one flows of transformations with infinite ergodic index},
author = {Alexandre I. Danilenko and Kyewon K. Park},
journal= {arXiv preprint arXiv:0910.2856},
year = {2009}
}