Infinite ergodic index ℤd -actions in infinite measure
Muehlegger, E. ; Raich, A. ; Silva, C. ; Touloumtzis, M. ; Narasimhan, B. ; Zhao, W.
Colloquium Mathematicae, Tome 79 (1999), p. 167-190 / Harvested from The Polish Digital Mathematics Library
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We construct infinite measure preserving and nonsingular rank one ℤd-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 ℤd-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 ℤd-actions for each Krieger ratio set type with individual basis transformations with similar properties.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210755 
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     title = {Infinite ergodic index $$\mathbb{Z}$^d$ -actions in infinite measure},
     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {167-190},
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Muehlegger, E.; Raich, A.; Silva, C.; Touloumtzis, M.; Narasimhan, B.; Zhao, W. Infinite ergodic index $ℤ^d$ -actions in infinite measure. Colloquium Mathematicae, Tome 79 (1999) pp. 167-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i2p167bwm/

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