On statistical measure theory

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	On statistical measure theory
	Bao, Lingxin ; Cheng, Lixin ; Cheng LX(程立新)
刊名	http://dx.doi.org/10.1016/j.jmaa.2013.05.039
	2013
关键词	CONVERGENCE SUMMABILITY SEQUENCES SPACES
英文摘要	Natural Science Foundation of China [11071021]; The purpose of this paper is to unify various kinds of statistital convergence by statistical measure convergence and to present Jordan decomposition of finitely additive measures. It is done through dealing with the most generalized statistical convergence-ideal convergence by applying geometric functional analysis and Banach space theory. We first show that for each type of ideal l(subset of 2(N)) convergence, there exists a set s of statistical measures such that the measure s-convergence is equivalent to the statistical convergence. To search for Jordan decomposition of measures of statistical type, we show that the subspace X-l (span) over bar{chi(A) : A is an element of l} is an ideal of the space l(infinity) in the sense of Banach lattice, hence the quotient space l(infinity)/X-l is isometric to a C(K) space. We then prove that a statistical measure has a Jordan decomposition if and only if its corresponding functional is norm-attaining on l(infinity), and which in turn induces an approximate null-ideal preserved Jordan decomposition theorem of finitely additive measures. Finally, we show this characterization and the approximate decomposition theorem are true for finitely additive measures defined on a general measurable space. (C) 2013 Elsevier Inc. All rights reserved.
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91209]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Bao, Lingxin,Cheng, Lixin,Cheng LX. On statistical measure theory[J]. http://dx.doi.org/10.1016/j.jmaa.2013.05.039,2013.
APA	Bao, Lingxin,Cheng, Lixin,&程立新.(2013).On statistical measure theory.http://dx.doi.org/10.1016/j.jmaa.2013.05.039.
MLA	Bao, Lingxin,et al."On statistical measure theory".http://dx.doi.org/10.1016/j.jmaa.2013.05.039 (2013).