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This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.

Probability: A Graduate Course

Introductory Measure Theory.- Random Variables.- Inequalities.- Characteristic Functions.- Convergence.- The Law of Large Numbers.- The Central Limit Theorem.- The Law of the Iterated Logarithm.- Limit Theorems; Extensions and Generalizations.- Martingales.