Infinite ergodic index $ℤ^d$ -actions in infinite measure
Colloquium Mathematicum, Tome 82 (1999) no. 2, pp. 167-190
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Affiliations des auteurs :
E. Muehlegger 1 ; A. Raich 1 ; C. Silva 1 ; M. Touloumtzis 1 ; B. Narasimhan 1 ; W. Zhao 1
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author = {E. Muehlegger and A. Raich and C. Silva and M. Touloumtzis and B. Narasimhan and W. Zhao},
title = {Infinite ergodic index $\ensuremath{\mathbb{Z}}^d$ -actions in infinite measure},
journal = {Colloquium Mathematicum},
pages = {167--190},
year = {1999},
volume = {82},
number = {2},
doi = {10.4064/cm-82-2-167-190},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-82-2-167-190/}
}
TY - JOUR AU - E. Muehlegger AU - A. Raich AU - C. Silva AU - M. Touloumtzis AU - B. Narasimhan AU - W. Zhao TI - Infinite ergodic index $ℤ^d$ -actions in infinite measure JO - Colloquium Mathematicum PY - 1999 SP - 167 EP - 190 VL - 82 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-82-2-167-190/ DO - 10.4064/cm-82-2-167-190 LA - en ID - 10_4064_cm_82_2_167_190 ER -
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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
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