Schaums Outline of Real Variables Lebesgue Measure And Integration With Applications to Fourier Series by Murray R Spiegel

One of the most important contributions to modern mathematical analysis is the theory of measure and integration developed by Henri Lebesgue during the early years of the 20th century. Lebesgue measure and integration has many advantages over ordinary Riemann integration from the point of view of application as well as theory. It is an indispensable part of the foundations of various fields as, for example, the theory of probability and statistics and Fourier series.

A superb text on the fundamentals of Lebesgue measure and integration.
This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.

This Schaum's Study Guide is the perfect tool for getting a handle on statistics. Fully stocked with solved problemsÑ508 of themÑit shows you how to work problems that may not have been fully explained in class. Plus you get 694 additional problems to use for practice, with answers at the back of the book

This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and engineering. The author presents complex concepts in a succinct manner, making otherwise intimidating material approachable to undergraduates who are not necessarily studying mathematics as their major. Throughout, readers will learn how probability serves as the language in a variety of exciting fields. Specific applications covered include the coupon collector’s problem, Monte Carlo integration in finance, data compression in information theory, and more.