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Hutchison度量完备的充要条件
引用本文:奚李峰. Hutchison度量完备的充要条件[J]. 应用数学学报, 1998, 21(3): 437-444
作者姓名:奚李峰
作者单位:武汉大学数学系!武汉,430072
摘    要: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。

关 键 词:Hutchison度量 完备性 充要条件 距离空间

NECESSARY AND SUFFICIENT CONDITION FOR COMPLETENESS OF HUTCHISON METRIC
XI LIFENG. NECESSARY AND SUFFICIENT CONDITION FOR COMPLETENESS OF HUTCHISON METRIC[J]. Acta Mathematicae Applicatae Sinica, 1998, 21(3): 437-444
Authors:XI LIFENG
Abstract: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.
Keywords:Fractal   Hutchison's metric   completeness
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