Groups, measures, and the NIP

Hrushovski, Ehud¹ ; Peterzil, Ya’acov² ; Pillay, Anand³

¹ Hebrew University of Jerusalem, Department of Mathematics, Jerusalem, Israel
² University of Haifa, Department of Mathematics and Computer Science, Haifa, Israel
³ University of Illinois, Department of Mathematics, Altgeld Hall, 1409 W Green Street Urbana, IL 61801, and University of Leeds, School of Mathematics, Leeds, LS2 9JT England

Journal of the American Mathematical Society, Tome 21 (2008) no. 2, pp. 563-596

Résumé

We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’s conjectures relating definably compact groups $G$ in saturated $o$-minimal structures to compact Lie groups. We also prove some other structural results about such $G$, for example the existence of a left invariant finitely additive probability measure on definable subsets of $G$. We finally introduce the new notion of “compact domination" (domination of a definable set by a compact space) and raise some new conjectures in the $o$-minimal case.

Détail

DOI : 10.1090/S0894-0347-07-00558-9

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