中文摘要：

研究了定义在完备的可分度量空间上具有概率的无限迭代函数系统的遍历性质，证明了该系统的惟一进历性，推广了Elton的遍历定理。其证明初等简洁，不依赖于鞅论中的较为深刻的极限定理和Banach极限技术。

英文摘要：

This study was designed to elucidate the ergodic properties of infinite iterated function systems with probabilities on complete separable metric space and prove the unique ergodicity for the system, which would further extend Elton＇s ergodic theorem. The proofs were simple and elementary and did not reply on the profound limit theorem on martingale theory as well as Banaeh limit techenique.