The Riemann, Lebesgue and Generalized Riemann Integrals aims at the definition and development of the Henstock-Kurzweil integral and those of the McShane integral in the real line. The developments are as simple as the Riemann integration and can be presented in introductory courses. The Henstock-Kurzweil integral is of super Lebesgue power while the McShane integral is of Lebesgue power. For bounded functions, however, the Henstock-Kurzweil, the McShane and the Lebesgue integrals are equivalent. Owing to their simple construction and easy access, the Generalized Riemann integrals will surely be familiar to physicists, engineers and applied mathematicians. Each chapter of the book provides a good number of solved problems and counter examples along with selected problems left as exercises.

Preface / The Riemann Integral / The Lebesgue Measure / The Lebesgue Integral / Functions of Bounded Variation / Semi-continuous Functions / Tagged Gauge Partitions / The Henstock-Kurzweil Integral / The Absolute Integrals / The Riemann Integral Revisited / The HK-Integral on Sets / Author’s Related Publications / Bibliography / Index.

Undergraduate – Postgraduate Students in Mathematics