Abstract

The paper develops a second-moment lower bound for the probability of a union and applies it to strengthen the divergence direction of the Borel–Cantelli lemma. Equations (4)–(6) are the proof-critical source used in the dependence graph.

Role in dependence graphs

Proof-critical source

Bounded trajectories of quasi-rays

This paper is included only for the following marked statement:

  • Second-moment union lower bound · printed pp. 180–181, equations (4)–(6)Bounds the measure of a finite union from below by the squared sum of the event measures divided by the sum of pairwise intersections; Kleinbock–Wang use its limsup form as Lemma 3.1.

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