[1] Ouyang Yao, Li Jun,. Some properties of monotone set functions definedby Choquet integral [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 423-426. [doi:10.3969/j.issn.1003-7985.2003.04.025]

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Some properties of monotone set functions definedby Choquet integral()

Choquet 积分定义的单调集函数的几个遗传性质

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

423-426

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

Some properties of monotone set functions definedby Choquet integral

Choquet 积分定义的单调集函数的几个遗传性质

Author(s):

Ouyang Yao;  Li Jun

Department of Mathematics, Southeast University, Nanjing 210096, China

欧阳耀;  李军

东南大学数学系, 南京 210096

Keywords:

non-additive measure;  monotone set function;  Choquet integral

非可加测度;  单调集函数;  Choquet积分

PACS:

O159

DOI:

10.3969/j.issn.1003-7985.2003.04.025

Abstract:

In this paper, some properties of the monotone set function defined by the Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as weak null-additivity, strong order continuity, property(s)and pseudometric generating property, etc., are preserved by the new set function. It is also shown that C-integrability assumption is inevitable for the preservations of strong order continuous and pseudometric generating property.

讨论了Choquet积分定义的单调集函数的几个遗传性质.证明了Choquet积分定义的新的单调集函数遗传了原来集函数的几个重要的结构特性, 如弱零可加性、 强序连续性、性质(S)和伪距离生成性质等.最后通过2个例子说明了当被积函数不是C可积时, 强序连续性和伪距离生成性质将不再被保留.

References:

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Memo

Memo:

Biographies: Ouyang Yao(1973—), male, graduate; Li Jun(corresponding author), male, doctor, professor, lijun@seu.edu.cn.

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