The automorphism group of the Gaussian measure cannot act pointwise
| dc.creator | Glasner, E. | |
| dc.creator | Tsirelson, B. | |
| dc.creator | Weiss, B. | |
| dc.date | 2003-11-25 | |
| dc.date | 2004-03-24 | |
| dc.date.accessioned | 2026-07-07T06:29:03Z | |
| dc.date.available | 2026-07-07T06:29:03Z | |
| dc.description | Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for Boolean G-actions. We show that in full generality this theorem does not hold for actions of Polish groups. In particular there is no Borel model for the Polish automorphism group of a Gaussian measure. In fact, we show that this group as well as many other Polish groups do not admit any nontrivial Borel measure preserving actions. | |
| dc.description | v2 (final), 18 pages. Added: remarks 1.4, 1.5, 1.9, 3.6 (supplemented); Appendix B; some historical background; refs 1, 5, 12, 18, 20-25, 29, 32 | |
| dc.identifier | https://arxiv.org/abs/math/0311450 | |
| dc.identifier | http://arxiv.org/abs/math/0311450 | |
| dc.identifier | Israel Journal of Mathematics 148 (2005), 305-329. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97900 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Probability | |
| dc.subject | 28D15; 28C20, 60A10, 60G15, 37B05 | |
| dc.title | The automorphism group of the Gaussian measure cannot act pointwise | |
| dc.type | text |