报告题目：Comparison property for amenable group actions
报告摘要：Let a countable discrete group G act on a zero dimensional compact metric space X. We say that the action admits comparison if for any clopen sets A and B, the condition, that for every G-invariant measure m on X we have that the sharp inequality m(A)<m(B), implies that A is subequivalent to B, that is, there exists a finite clopen partition A_1,.., A_k for A, and elements g_1,..., g_k in G such that g_1(A_1),..., g_k(A_k) are disjoint clopen subsets of B. We prove this property for actions of groups whose every finitely generated subgroup has subexponential growth. This is a joint work with Professor Tomasz Downarowicz.