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Originating from the author's own graduate course at the University of North carolina, this material has been thoroughly tried and tasted over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue intregation, limit theorems in probability, martigales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercies provided.