Hutchison度量完备的充要条件

NECESSARY AND SUFFICIENT CONDITION FOR COMPLETENESS OF HUTCHISON METRIC

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率测度全体，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．

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.