Front Cover -- A Primer of Real Functions -- Copyright Page -- Preface to the Fourth Edition -- Preface to the Third Edition -- Contents -- Chapter 1. Sets -- 1 Sets -- 2 Sets of real numbers -- 3 Countable and uncountable sets -- 4 Metric spaces -- 5 Open and closed sets -- 6 Dense and nowhere dense sets -- 7 Compactness -- 8 Convergence and completeness -- 9 Nested sets and Baire's theorem -- 10 Some applications of Baire's Theorem -- 11 Sets of measure zero -- Chapter 2. Functions -- 12 Functions -- 13 Continuous functions -- 14 Properties of continuous functions -- 15 Upper and lower limits -- 16 Sequences of functions -- 17 Uniform convergence -- 18 Pointwise limits of continuous functions -- 19 Approximations to continuous functions -- 20 Linear functions -- 21 Derivatives -- 22 Monotonic functions -- 23 Convex functions -- 24 Infinitely differentiable functions -- Chapter 3. Integration -- 25 Lebesgue measure -- 26 Measurable functions -- 27 Definition of the Lebesgue integral -- 28 Properties of Lebesgue integrals -- 29 Applications of the Lebesgue integral -- 30 Stieltjes integrals -- 31 Applications of the Stieltjes integral -- 32 Partial sums of infinite series -- Answers to Exercises -- Index -- Back Cover.