Wiley Series in Probability and Statistics: The Theory of Measures and Integration

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This accessible survey of measure theory is designed for students and researchers in mathematics, statistics, and physics. A foundational understanding of measure theory is essential for grasping advanced concepts in probability and analysis. The text illuminates fundamental ideas of the subject, providing a solid theoretical background for further inquiry. Eric Vestrup presents classical measure and integration theory's major results in a clear and rigorous manner. In addition to core topics, the author discusses extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, all in a user-friendly style. Chapters cover areas such as Measurable Functions, Lp Spaces, the Radon-Nikodym Theorem, and Products of Measure Spaces. Each section concludes with exercises of varying difficulty, from simple "finger exercises" to more substantial challenges, with detailed hints provided for the latter. Vestrup's approach targets those who appreciate thoroughness in proofs and notation. This text serves as an excellent primary resource for graduate students in mathematics, statistics, and physics, as well as strong undergraduates and practicing researchers, making it a valuable asset for real analysis sequences focused on measure theory and advanced courses in probability and statistics.