群作用下的Khintchine回归定理

A General Khintchine Recurrence Theorem

利用积分论得出保测变换的一个基本性质及庞加莱回归定理的一个等价命题,建立概率保测系统概念,并推广了Khintchine回归定理,利用一般的Khintchine回归定理得到了回归集的一些性质。

A simple property of measure-preserving transformation and one equivalent proposition of Poincare recurrence theorem are obtained by using integral theory. The paper establishes the concept of measure-preserving system and extends the recunence theorem. Some properties of return sets are obtained by using the general Khintchine recurrence theorem.