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Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.

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• Preface
• 1 The completeness of the reals
• 2 Null sets
• 3 The Lebesgue integral on R
• 4 The Lebesgue integral on Rk
• 5 The convergence theorems
• 6 Measurable functions and Lebesgue measure
• 7 The spaces Lp
• Appendix: the elements of topology
• Solutions
• References
• Index