Functional Erdős-Rényi laws for processes indexed by sets (Q1365719)

Consider a process \(\{X(A)\}\) indexed by sets \(A\) from a collection of sets \({\mathcal A}\). Assuming that \(\{X(A)\}\) has independent increments and obeys a large deviation principle, the authors prove a functional Erdős-Rényi type theorem. Some previous results are shown to be included in this general theorem.