Borel-Cantelli引理的一个推论

2010-02-23 06:23王福彪
陕西科技大学学报 2010年6期
关键词:财经大学南京参考文献

王福彪

(南京财经大学数学学院, 江苏 南京 210046)

在证明定理2之前首先证明一个引理.

(1)

定理2的证明先证左边不等式,由Cauchy-Schwarz不等式得

由引理得以下不等式

参考文献

[1] Chungrong Feng, Liangpan Li, Jian Shen.On the Borel-Cabtelli lemma and its generalization[J]. C.R.Acad.Ser.,2009,347:1 313-1 316.

[2] XIE Yuquan.Abilateral inequality on the Borel-Cantelli lemma[J]. Statist.Probab.Lett., 2008,78:2 052-2 057.

[3] Hu Shuhe,Wang Xuejun,Li Xiaoqin,etal.. Comments on paper:a bilateral inequality on the Borel-Cantelli lemma[J].Statist.Probab.Lett., 2009,79:889-893.

[4] Petrov.V.V. A generalization of the Borel-Cantelli lemma[J]. Lett, 2004,(67):233-239.

[5] Kochen-Stone. A note on the Borel-Cantelli lemma[J]. Illinois Journal of Mathematics,1964,8:248-251.

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