Bochner积分的推广

(Department of Mathematics, Wuhan University, Wuhan 430072)
(Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences,Whuan 430071)

摘要：

引进偏Bochner积分的概念.证明了在不可分情形下，偏Bochner积分与Bochner积分有本质的差异.作为应用，通过向量测度空间用偏Bochner积分给出了Radon-Nikodym性质的一个刻划.

关键词: 偏Ｂｏｃｈｎｅｒ积分, Ｂｏｃｈｎｅｒ积分, 范定集, ＲａｄｏｎＮｉｋｏｄｙｍ性质．

Abstract:

Partial Bochner integrals are introduced and studied. And, we present a characterization of the Radon-Nikodym property by means of the integral.

Key words: ＰａｒｔｉａｌＢｏｃｈｎｅｒｉｎｔｅｇｒａｌｓ, Ｂｏｃｈｎｅｒｉｎｔｅｇｒａｌｓ, Ｎｏｒｍｉｎｇｓｅｔｓ, ｔｈｅＲａｄｏｎＮｉｋｏｄｙｍｐｒｏｐｅｒｔｙ．

中图分类号:

赵俊峰陈泽乾. Bochner积分的推广[J]. 数学物理学报, 1999, 19(1): 101-106.

Zhao Junfeng Chen Zeqian . An Extension of Bochner Integrals[J]. Acta mathematica scientia,Series A, 1999, 19(1): 101-106.

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