The book has been designed as a supplement to all current standard textbooks or as a textbook for a formal course in real variables. It should also prove useful in other courses in mathematics which require a knowledge of Lebesgue theory. In addition it should be of value to those readers in science and engineering, as well as mathematics, who desire an introduction to this important theory.
Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principles so vital to effective learning. Numerous proofs of theorems and derivations of basic results are included among the solved problems. The large number of supplementary problems serve as a review and possible extension of the material of each chapter.