Comptes Rendus
Probability Theory
On the Borel–Cantelli lemma and its generalization
[Sur le lemme de Borel–Cantelli et sa généralisation]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1313-1316.

Let {An}n=1 be a sequence of events on a probability space (Ω,F,P). We show that if limmn=1mwnP(An)= where each wnR, then

P(lim supAn)lim supn(k=1nwkP(Ak))2i=1nj=1nwiwjP(AiAj).

Soit {An}n=1 une séquence d'événements dans un éspace de probabilité (Ω,F,P). On montre que, si limmn=1mwnP(An)= où chaque wnR, alors

P(lim supAn)lim supn(k=1nwkP(Ak))2i=1nj=1nwiwjP(AiAj).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.09.011

Chunrong Feng 1, 2 ; Liangpan Li 1, 3 ; Jian Shen 3

1 Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
2 Department of Mathematical Sciences, Loughborough University, LE11 3TU, UK
3 Department of Mathematics, Texas State University, San Marcos, TX 78666, USA
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Chunrong Feng; Liangpan Li; Jian Shen. On the Borel–Cantelli lemma and its generalization. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1313-1316. doi : 10.1016/j.crma.2009.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.011/

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