This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability
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<P><STRONG>Measure Theory and Fine Properties of Functions, Revised Edition</STRONG> provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff...
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<p>The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject...
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<p>This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian...
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