On the Borel-Cantelli Lemma and its Generalization

2009/10/01 by Chunrong Feng, Feng, Chunrong, Liangpan Li +3
Economics, Econometrics and Finance · Engineering · Mathematics · #60C05 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0910.0067

openalex publication_date 2009/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \A_n\_n=1^∞ be a sequence of events on a probability space (Ω,F,P). We show that if lim_m→∞∑_n=1^mw_nP(A_n)=∞ where each w_n∈ℝ, then P(\limsup A_n)≥\limsup_n→∞ \frac(∑_k=1ⁿw_kP(A_k))²∑_i=1ⁿ∑_j=1ⁿw_iw_jP(A_i∩ A_j).

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