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Infinite ergodic index $ℤ^d$ -actions in infinite measure

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Muehlegger E. J., Raich A. S., Silva C. E., Touloumtzis M. P., Narasimhan B., Zhao W.

Colloquium Mathematicum

1999

tom 82

nr 2

167-190

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 products of all orders, hence infinite ergodic index. We generalize this example to obtain a stronger condition called power weakly mixing. The last examples are nonsingular $ℤ^d$-actions for each Krieger ratio set type with individual basis transformations with similar properties.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Muehlegger E. J.

1 Narasimhan B.

1 Raich A. S.

1 Silva C. E.

1 Touloumtzis M. P.

1 Zhao W.

1 1999

Wyniki wyszukiwania

Infinite ergodic index $ℤ^d$ -actions in infinite measure