Hutchison度量完备的充要条件

距离空间Ｘ上，以Ｍ（Ｘ）记定义在Ｘ的Ｂｏｒｅｌ域上的具有有界支撑的概度测度全体，Ｒ（Ｘ）记Ｍ（Ｘ）中所有Ｒａｄｏｎ测度，Ｍ（Ｘ），Ｒ（Ｘ）均赋予Ｈｕｔｃｈｉｓｏｎ度量，本文得到：Ｒ（Ｘ）完备当且仅当Ｘ完备且有界，若Ｘ可分，则：Ｍ（Ｘ）完备当且仅当Ｘ完备且有界。

NECESSARY AND SUFFICIENT CONDITION FOR COMPLETENESS OF HUTCHISON METRIC

For metric space X, by M(X) we mean the set of Borel probability measures over X with bounded support, and by R(X) the set of Radon measures in M(X).M(X), R(X) are endowed with Hutchison metric. In this paper, the following results weregot: R(X) is complete if and only if X is complete and bounded. In case that X is seperable,then M(X) is complete if and only if X is complete and bounded.