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Infinite ergodic index ℤ d -actions in infinite measure

E. Muehlegger;  A. Raich;  C. Silva;  M. Touloumtzis;  B. Narasimhan;  W. Zhao — 1999

Colloquium Mathematicae

We construct infinite measure preserving and nonsingular rank one ℤ d -actions. The first example is ergodic infinite measure preserving but with nonergodic, infinite conservative index, basis transformations; in this case we exhibit sets of increasing finite and infinite measure which are properly exhaustive and weakly wandering. The next examples are staircase rank one infinite measure preserving ℤ d -actions; for these we show that the individual basis transformations have conservative ergodic Cartesian...

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