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|GAIL IVANOFF, Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada|
We give an appropriate framework and definitions for the theory of set-indexed martingales. Compensators and quadratic variation processes will be defined, and used to develop set-indexed analogues of the classical martingale characterizations of the Poisson process and Brownian motion. Sufficient conditions will be given in terms of compensators for a Poisson convergence theorem and in terms of quadratic variation processes for a martingale central limit theorem. Applications to set-indexed empirical processes will be discussed.