Nikitin's Law of Repeated Inevitability: A New Probabilistic Theorem Bridging Modal Logic and Probability Theory (English)

This work formulates a universal sufficient criterion for the convergence of event probabilities to one in classes of probabilistic models with dependence and memory effects. Unlike classical results such as the Borel–Cantelli lemma and the Kochen–Stone theorem, the proposed condition does not require independence of events or control over pairwise covariances. The criterion is based on a natural asymptotic constraint involving the decay of probabilities and the memory function. A counterexample is provided to demonstrate the necessity of the condition: when it fails, the probability of event realization tends to zero. The results are applicable to the theory of random graphs with cumulative effects, the dynamics of network processes, and probabilistic models with decaying dependence.