Borel-Cantelli引理的一個(gè)推論

王福彪

(南京財(cái)經(jīng)大學(xué)數(shù)學(xué)學(xué)院, 江蘇 南京 210046)

在證明定理2之前首先證明一個(gè)引理.

(1)

定理2的證明先證左邊不等式，由Cauchy-Schwarz不等式得

由引理得以下不等式

參考文獻(xiàn)

[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.