This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition.



This text is based on the author’s experience teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student in the class, considering the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student,


while simultaneously challenging the more talented students through the exercises.


Chapters seven through ten assume the students have achieved some expertise in the subject. These chapters' theorems, examples, and exercises require greater sophistication and mathematical maturity for complete understanding.



In addition to the standard topics, the text includes issues not always included in comparable texts.






Chapter 6 contains a section on the Riemann-Stieltjes integral and proof of Lebesgue’s theorem, providing necessary and sufficient conditions for Riemann's integrability.




Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces.




Cchapter 8 contains a proof of the Weierstrass approximation theorem using the method of


aapproximate identities.





Including the Fourier series in the text allows the student to gain some exposure to this vital subject.




The final chapter includes a detailed treatment of the Lebesgue measure and the Lebesgue integral, using the inner and outer bar.




The exercises at the end of each section reinforce the concepts.




Notes provide historical comments or discuss additional topics.