# Infinite ergodic index ${\mathbb{Z}}^{d}$ -actions in infinite measure

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

Colloquium Mathematicae (1999)

- Volume: 82, Issue: 2, page 167-190
- ISSN: 0010-1354

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topMuehlegger, E., et al. "Infinite ergodic index $ℤ^d$ -actions in infinite measure." Colloquium Mathematicae 82.2 (1999): 167-190. <http://eudml.org/doc/210755>.

@article{Muehlegger1999,

abstract = {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.},

author = {Muehlegger, E., Raich, A., Silva, C., Touloumtzis, M., Narasimhan, B., Zhao, W.},

journal = {Colloquium Mathematicae},

keywords = {infinite measure preserving transformation; conservative index basis transformation},

language = {eng},

number = {2},

pages = {167-190},

title = {Infinite ergodic index $ℤ^d$ -actions in infinite measure},

url = {http://eudml.org/doc/210755},

volume = {82},

year = {1999},

}

TY - JOUR

AU - Muehlegger, E.

AU - Raich, A.

AU - Silva, C.

AU - Touloumtzis, M.

AU - Narasimhan, B.

AU - Zhao, W.

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

JO - Colloquium Mathematicae

PY - 1999

VL - 82

IS - 2

SP - 167

EP - 190

AB - 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.

LA - eng

KW - infinite measure preserving transformation; conservative index basis transformation

UR - http://eudml.org/doc/210755

ER -

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