Synopses & Reviews
"In scope and choice of subject matter," declared the
Bulletin of the American Mathematics Society, "this text is nicely calculated to suit the needs of introductory classes in real variable theory." A balanced treatment, it covers all of the fundamentals, from the real number system and point sets to set theory and metric spaces.
Starting with a brief exposition of the ideas and methods of deductive logic, the text proceeds to the postulates of Peano for the natural numbers and outlines a method for constructing the real number system. Subsequent chapters explore functions and their limits, the properties of continuous functions, fundamental theorems on differentiation, the Riemann integral, and uniform convergence. Additional topics include ordinary differential equations, the Lebesgue and Stieltjes integrals, and transfinite numbers. Useful, well-chosen lists of references to the literature conclude each chapter.
Synopsis
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Synopsis
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Table of Contents
PrefaceChapter I. INTRODUCTIONChapter II. THE REAL NUMBER SYSTEMChapter III. POINT SETSChapter IV. FUNCTIONS AND THEIR LIMITS. PROPERTIES OF CONTINOUS FUNCTIONSChapter V. FUNDAMENTAL THEOREMS ON DIFFERENTIATIONChapter VI. THE RIEMANN INTEGRALChapter VII. UNIFOEM CONVERGENCEChapter VIII. FUNCTIONS DEFINED IMPLICITLY Chapter IX. ORDINARY DIFFERENTIAL EQUATIONSChapter X. THE LEBESGUE INTEGRAL Chapter XI. THE LEBESGUE INTEGRAL (continued)Chapter XII. THE STIELTJES INTEGRALChapter XIII THE THEORY OF SETS AND TRANSFINITE NUMBERSChapter XIV. METRIC SPACESIndex