Wilcox H.J., Myers D.L. An Introduction to Lebesgue Integration and Fourier Series

Robert E. Krieger Publishing Company, 1978. — 159 p.Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.
This book arose out of our desire to present an introduction to Lebesgue Integration and Fourier Series in the second semester of our real variables course at Wellesley College. We found that most undergraduate texts do not cover these topics, or do so only in a cursory way. Graduate texts, we felt, lack motivation and depend on a level of sophistication not attained by most undergraduates.
We feel this text could be used for a course lasting one semester or less (there are several optional sections, marked with an asterix, which could easily be omitted). We assume knowledge of advanced calculus, including the notions of compactness, continuity , uniform convergence aad Riemann integration (i.e ., a usual one-semester undergraduate course in advanced calculus). Therefore, the book would be suitable for advanced undergraduates and beginning graduate students.