Let be an -categorical structure and assume that has no algebraicity and has weak elimination of imaginaries. Generalizing classical theorems of de Finetti and Ryll-Nardzewski, we show that any ergodic, -invariant measure on is a product measure. We also investigate the action of on the compact space of linear orders on . If we assume moreover that the action is transitive, we prove that the action either has a fixed point or is uniquely ergodic.
Soit une structure -catégorique sans algébricité et éliminant faiblement les imaginaires. En généralisant des théorèmes classiques de de Finetti et de Ryll-Nardzewski, nous démontrons que toute mesure -invariante et ergodique sur est une mesure produit. Nous étudions également l’action de sur l’espace compact des ordres totaux sur . Sous l’hypothèse supplémentaire que l’action est transitive, nous démontrons que l’action soit est uniquement ergodique, soit admet un point fixe.
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Keywords: Invariant measures, uniquely ergodic, linear orders, $\aleph _0$-categorical, de Finetti theorem
Mot clés : Mesures invariantes, uniquement ergodique, ordres totaux, $\aleph _0$-catégorique, théorème de de Finetti
Colin Jahel 1; Todor Tsankov 2
@article{JEP_2022__9__155_0, author = {Colin Jahel and Todor Tsankov}, title = {Invariant measures on products and on the~space of linear orders}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {155--176}, publisher = {\'Ecole polytechnique}, volume = {9}, year = {2022}, doi = {10.5802/jep.180}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.180/} }
TY - JOUR AU - Colin Jahel AU - Todor Tsankov TI - Invariant measures on products and on the space of linear orders JO - Journal de l’École polytechnique — Mathématiques PY - 2022 SP - 155 EP - 176 VL - 9 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.180/ DO - 10.5802/jep.180 LA - en ID - JEP_2022__9__155_0 ER -
%0 Journal Article %A Colin Jahel %A Todor Tsankov %T Invariant measures on products and on the space of linear orders %J Journal de l’École polytechnique — Mathématiques %D 2022 %P 155-176 %V 9 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.180/ %R 10.5802/jep.180 %G en %F JEP_2022__9__155_0
Colin Jahel; Todor Tsankov. Invariant measures on products and on the space of linear orders. Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 155-176. doi : 10.5802/jep.180. https://jep.centre-mersenne.org/articles/10.5802/jep.180/
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