Geodesic
On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 136-147

Voir la notice de l'article provenant de la source Cambridge University Press

Product type equivalence relations are hyperfinite measured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property $\text{A}$ . This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper.
DOI : 10.4153/CMB-2011-132-4
Mots-clés : 37A20, 37A35, 46L10, property A, hyperfinite equivalence relation, non-product type 
Munteanu, Radu-Bogdan. On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 136-147. doi: 10.4153/CMB-2011-132-4
@article{10_4153_CMB_2011_132_4,
     author = {Munteanu, Radu-Bogdan},
     title = {On {Constructing} {Ergodic} {Hyperfinite} {Equivalence} {Relations} of {Non-Product} {Type}},
     journal = {Canadian mathematical bulletin},
     pages = {136--147},
     year = {2013},
     volume = {56},
     number = {1},
     doi = {10.4153/CMB-2011-132-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-132-4/}
}
TY  - JOUR
AU  - Munteanu, Radu-Bogdan
TI  - On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 136
EP  - 147
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-132-4/
DO  - 10.4153/CMB-2011-132-4
ID  - 10_4153_CMB_2011_132_4
ER  - 
%0 Journal Article
%A Munteanu, Radu-Bogdan
%T On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type
%J Canadian mathematical bulletin
%D 2013
%P 136-147
%V 56
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-132-4/
%R 10.4153/CMB-2011-132-4
%F 10_4153_CMB_2011_132_4

[1] [1] Billingsley, P., Probability and measure. Third ed., Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, 1995. Google Scholar

[2] [2] Connes, A. and Woods, E. J., Approximately transitive flows and ITPFI factors. Ergodic Theory Dynam. Systems 5 (1985), no. 2, 203–236. Google Scholar

[3] [3] Dooley, A. H. and Hamachi, T., Markov odometer actions not of product type. Ergodic Theory Dynam. Systems 23 (2003), no. 3, 813–829. Google Scholar | DOI

[4] [4] Elliott, G. A. and Giordano, T., Every approximately transitive amenable action of a locally compact group is a Poisson boundary. C. R. Math. Acad. Sci. Soc. R. Can. 21 (1999), no. 1, 9–15. Google Scholar

[5] [5] Feldman, J. and Moore, C. C., Ergodic equivalence relations, cohomology, and von Neumann algebras. I. Trans. Amer. Math. Soc. 234 (1977), no. 2, 289–324. Google Scholar | DOI

[6] [6] Feldman, J. and Moore, C. C., Ergodic equivalence relations, cohomology, and von Neumann algebras. II. Trans. Amer. Math. Soc. 234 (1977), no. 2, 325–359. Google Scholar | DOI

[7] [7] Giordano, T. and Handelman, D., Matrix-valued random walks and variations on property AT. Mönster J. Math. 1 (2008), 15–72. Google Scholar

[8] [8] Hamachi, T. and Osikawa, M., Ergodic groups of automorphisms and Krieger's theorems. Seminar on Mathematical Sciences, 3, Keio University, Department of Mathematics, Yokohama, 1981. Google Scholar

[9] [9] Katznelson, Y. and B.Weiss, The classification of nonsingular actions, revisited. Ergodic Theory Dynam. Systems 11 (1991), no. 2, 333–348. Google Scholar

[10] [10] Krieger, W., On nonsingular transformations of a measure space. I, II. Z.Wahrsheinlichkeitstheorie und Verw. Gebiete 11 (1969), 83–97; ibid. 11 (1969), 98–119. Google Scholar

[11] [11] Krieger, W., On the infinite product construction of non-singular transformations of a measure space. Invent. Math. 15 (1972), 144–163. Google Scholar | DOI

[12] [12] Krieger, W., Erratum to: “On the infinite product construction of non–singular transformations of a measure space” (Invent. Math. 15 (1972), 144–163). Invent Math. 26 (1974), 323–328. Google Scholar

[13] [13] Keane, M., Entropy in ergodic theory. In: Entropy, Princeton Ser. Appl. Math., Princeton University Press, Princeton, NJ, 2003, pp. 329–335. Google Scholar

[14] [14] Méla, X. and Petersen, K., Dynamical properties of the Pascal adic transformation. Ergodic Theory Dynam. Systems 25 (2005), no. 1, 227–256. Google Scholar | DOI

[15] [15] Munteanu, R-B. A non-product type non-singular transformation which satisfies Krieger's property A. arXiv:0912.2627v1. Google Scholar

Cité par Sources :