We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-4, author = {T. Hamachi and M. S. Keane and M. K. Roychowdhury}, title = {Finitary orbit equivalence and measured Bratteli diagrams}, journal = {Colloquium Mathematicae}, volume = {111}, year = {2008}, pages = {363-382}, zbl = {1172.37004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-4} }
T. Hamachi; M. S. Keane; M. K. Roychowdhury. Finitary orbit equivalence and measured Bratteli diagrams. Colloquium Mathematicae, Tome 111 (2008) pp. 363-382. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-2-4/