The purpose of this book is to give a straightforward and yet elementary introduction to measure and integration theory that is within the grasp of second or third year undergraduates. Indeed, apart from interest in the subject, the only prerequisites for Chapters 1–13 are a course on rigorous ε-δ analysis on the real line and basic notions of linear algebra and calculus in ℝn. The first few chapters form a concise (not to say minimalist) introduction to Lebesgue's approach to measure and integration, based on a 10-week, 30-hour lecture course for Sussex University mathematics undergraduates. Chapters 14–24 are more advanced and contain a selection of results from measure theory, probability theory and analysis. This material can be read linearly but it is also possible to select certain topics; see the dependence chart on page xi. Although more challenging than the first part, the prerequisites stay essentially the same and a reader who has worked through and understood Chapters 1–13 will be well prepared for all that follows. At some points, one or another concept from point-set topology will be (mostly superficially) needed; those readers who are not familiar with the topic can look up the basic results in Appendix B whenever the need arises.

Each chapter is followed by a section of Problems. They are not just drill exercises but contain variants, excursions from and extensions of the material presented in the text.