数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1492-1500.doi: 10.1016/S0252-9602(10)60141-5

• 论文 • 上一篇    下一篇

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

刘宁1, 2|叶永刚1   

  1. 1.School of Economics and Managements, Wuhan |University, Wuhan 430072, China
    2.Finance School, Hubei University of Economics, Wuhan 430205, China
  • 收稿日期:2008-09-05 修回日期:2009-01-04 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    Supported by Major Project Foundation of Philosophy and Social Sciences Research of Ministry of Education of P.R.China (07JHQ0003) and
    Hubei Research Center for Financial Development and Financial Security (2008D029).

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

 LIU Ning1, 2, XIE Yong-Gang1   

  1. 1.School of Economics and Managements, Wuhan |University, Wuhan 430072, China
    2.Finance School, Hubei University of Economics, Wuhan 430205, China
  • Received:2008-09-05 Revised:2009-01-04 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    Supported by Major Project Foundation of Philosophy and Social Sciences Research of Ministry of Education of P.R.China (07JHQ0003) and
    Hubei Research Center for Financial Development and Financial Security (2008D029).

摘要:

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

关键词: weak Orlicz space,   convergence theorem, conditional compactness

Abstract:

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

Key words: weak Orlicz space,   convergence theorem, conditional compactness

中图分类号: 

  • 46E30