Geodesic
Infinite ergodic index $ℤ^d$ -actions in infinite measure
Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 167-190.

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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.
DOI : 10.4064/cm-82-2-167-190

E. Muehlegger 1 ; A. Raich 1 ; C. Silva 1 ; M. Touloumtzis 1 ; B. Narasimhan 1 ; W. Zhao 1

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E. Muehlegger; A. Raich; C. Silva; M. Touloumtzis; B. Narasimhan; W. Zhao. Infinite ergodic index $ℤ^d$ -actions in infinite measure. Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 167-190. doi : 10.4064/cm-82-2-167-190. http://geodesic.mathdoc.fr/articles/10.4064/cm-82-2-167-190/

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