About Borel-Cantelli Lemma Exttetion And Applaction

Probablity theory to reseach on ecnomic finace engineering and other issues provid a framwork for a more systemitcs,so we study Borel-Cantelli lemma of probality theory is an important.this lemma has a very broad application.but the conditions of lemma are harsh,so we mainly focus on part two. In recent years, Borel-cantelli lemma have been deeply and thoroughly researched. See, for example, [17-18]and[22]. Inspired and motivated by their work, in this paper, we introduction several iterative methods and their corresponding application. Our paper is divided into three chapters.The first chapter is the introduction which is constituted by two parts. They introduce the recent work of the famous authors in this field and contain corresponding lemmasand definitions respectively.In the two chapter we can get general Borel-Cantelli lemma and its use, before we prove lemma we give several lemma and its several extension.In chapter three ,in the probablity theory space about extension Borel-Cantelli lemma then introduction extension Borel-Cantelli lemma and its application.Our results are new and can be viewed as generalizations and extensions of the corresponding results obtained in [16], [17] and [22].