自同态的半流的不变测度

Lnvariant Measure under an Endomorphism Semi flow

Ｏｘｔｏｂｙ－Ｕｌａｍ指出：在完备、可分的度量空间Ｍ上，存在非平凡的关于流｛Ｔｔ｝为不变的测度ｌｉｍｓｕｐｔ→∞１ｔ∫ｔ０ｆＫ（Ｔｓｘ０）ｄｓ＞０，对某点ｘ０∈Ｍ和紧集ＫＭ，ｆＫ是Ｋ的特征函数．本文把Ｏｘｔｏｂｙ－Ｕｌａｍ关于流的这一结果推广到半流的情形，给出结果的完整证明．

Oxtoby Ulam indicated necessary and sufficient condition for the existence of non trivial invariant measures under flow of a complete separable metric space.Our theorem in the case of semi flow which extends their result for flow,and a complete proof is given.