For any m-dependent sequence of events, the probability that at least one occurs is bounded below by 1 minus the exponential of the negative average probability per independent class.
On the Borel–Cantelli Lemmas, the Erdős–Rényi theorem, and the Kochen–Stone theorem
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A finite-sample Borel--Cantelli inequality under $m$-dependence
For any m-dependent sequence of events, the probability that at least one occurs is bounded below by 1 minus the exponential of the negative average probability per independent class.