Acta mathematica scientia, Series B >
WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS
Received date: 2008-09-05
Revised date: 2009-01-04
Online 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).
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
LIU Ning , XIE Yong-Gang . WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1492 -1500 . DOI: 10.1016/S0252-9602(10)60141-5
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