L'ensemble des paires de transformations ergodiques de l'intervalle peut être muni d'une structure borélienne standard. Nous montrons que la relation de conjugaison n'est pas borélienne dans cet espace, en fait est analytique complète. Notre construction montre aussi que les ensembles et sont des analytiques complets.
The set of pairs of transformations on the interval can be equipped with a standard Borel structure. We prove that the relation of conjugacy is not a Borel subset of this space, in fact it is complete analytic. Moreover, our construction proves that the two sets, , and are complete analytic sets.
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@article{CRMATH_2006__343_10_653_0, author = {Foreman, Matthew D. and Rudolph, Daniel J. and Weiss, Benjamin}, title = {On the conjugacy relation in ergodic theory}, journal = {Comptes Rendus. Math\'ematique}, pages = {653--656}, publisher = {Elsevier}, volume = {343}, number = {10}, year = {2006}, doi = {10.1016/j.crma.2006.09.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.09.011/} }
TY - JOUR AU - Foreman, Matthew D. AU - Rudolph, Daniel J. AU - Weiss, Benjamin TI - On the conjugacy relation in ergodic theory JO - Comptes Rendus. Mathématique PY - 2006 SP - 653 EP - 656 VL - 343 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.09.011/ DO - 10.1016/j.crma.2006.09.011 LA - en ID - CRMATH_2006__343_10_653_0 ER -
%0 Journal Article %A Foreman, Matthew D. %A Rudolph, Daniel J. %A Weiss, Benjamin %T On the conjugacy relation in ergodic theory %J Comptes Rendus. Mathématique %D 2006 %P 653-656 %V 343 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.09.011/ %R 10.1016/j.crma.2006.09.011 %G en %F CRMATH_2006__343_10_653_0
Foreman, Matthew D.; Rudolph, Daniel J.; Weiss, Benjamin. On the conjugacy relation in ergodic theory. Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 653-656. doi : 10.1016/j.crma.2006.09.011. http://archive.numdam.org/articles/10.1016/j.crma.2006.09.011/
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