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Basic propability theory
This book has been written for a first course in probability and was developed from lectures given at the University of Illinois during the last five years. Most of the students have been juniors, seniors, and beginning graduates, from the fields of mathematics, engineering and physics. The only formal prerequisite is calculus, but an additional degree of mathematical maturity may be helpful.
In talking about nondiscrete probability spaces, it is difficult to avoid measure-theoretic concepts. However, to develop extensive formal machinery from measure theory before going into probability (as is done in most graduate programs in mathematics) would be inappropriate for the particular audience to whom the book is addressed. Thus I have tried to suggest, when possible, the underlying measure-theoretic ideas, while emphasizing the probabilistic way of thinking, which is likely to be quite novel to anyone studying this subject for the first time.
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