A Modern Theory Of Integration (Relié)

This book gives an introduction to integration theory via the "generalized Riemann integral" due to Henstock and Kurzweil. The class of integrable functions coincides with those of Denjoy and Perron and includes all conditionally convergent improper integrals as well as the Lebesgue integrable functions. Using this general integral the author gives a full treatment of the Lebesgue integral on the line. The book is designed for students of mathematics and of the natural sciences and economics. An understanding of elementary real analysis is assumed, but no familiarity with topology or measure theory is needed. The author provides many examples and a large collection of exercises-many with solutions.