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An Introduction to Measure-Theoretic Probability (Hardcover, 2nd edition)
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An Introduction to Measure-Theoretic Probability (Hardcover, 2nd edition)
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An Introduction to Measure-Theoretic Probability, Second Edition,
employs a classical approach to teaching the basics of measure
theoretic probability. This book provides in a concise, yet
detailed way, the bulk of the probabilistic tools that a student
working toward an advanced degree in statistics, probability and
other related areas should be equipped with. This edition requires
no prior knowledge of measure theory, covers all its topics in
great detail, and includes one chapter on the basics of ergodic
theory and one chapter on two cases of statistical estimation.
Topics range from the basic properties of a measure to modes of
convergence of a sequence of random variables and their
relationships; the integral of a random variable and its basic
properties; standard convergence theorems; standard moment and
probability inequalities; the Hahn-Jordan Decomposition Theorem;
the Lebesgue Decomposition T; conditional expectation and
conditional probability; theory of characteristic functions;
sequences of independent random variables; and ergodic theory.
There is a considerable bend toward the way probability is actually
used in statistical research, finance, and other academic and
nonacademic applied pursuits. Extensive exercises and practical
examples are included, and all proofs are presented in full detail.
Complete and detailed solutions to all exercises are available to
the instructors on the book companion site. This text will be a
valuable resource for graduate students primarily in statistics,
mathematics, electrical and computer engineering or other
information sciences, as well as for those in mathematical
economics/finance in the departments of economics.
General
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