Integration Theory

This book contains the material from an introductory course on integration theory taught at ETH (the SwissFederal Institute ofTechnology) in Zurich. Students taking the course are in their third or fourth year of tertiary studies and therefore have had substantial prior exposure to mathematics. The course assumes some familiarity with the concepts presented in the preceding courses. Since this book is addressed to a wider audience and since different in stitutes have different programmes, the same assumptions cannot be made here. As explaining everything in detail would have resulted in a book of daunting dimensions, whose very size would discourage all but those of epic heroism and dedication, we have chosen a compromise: weexplain in detail in the text itself only those ideas which are essential to the development of the subject matter and we have appended a separate glossary of all def initions used, adding explanations and examples as needed. The reader is, however, expected to be familiar with the basic properties of the Riemann integral as well as with basic facts from point-set topology; the latter are especially needed for Chapter 5, 'Measures on Hausdorff Spaces'. We have chosen this course in order to preserve the character of an intro duction at an intermediate level, which should nevertheless be accessible to those with limited prior knowledge, who are willing to postpone questions on matters not central to the development of the theory.