Published paper
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.
Proof-critical source
Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle
This paper is included only for the following marked statement:
- Equations (4)–(6) · printed pp. 180–181Second-moment lower bound for finite unions used locally by Kleinbock–Wang.
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