Includes bibliographical references (p. 295-303) and index.
The One-Dimensional Henstock-Kurzweil Integral-- The Multiple Henstock-Kurzweil Integral-- Lebesgue Integrable Functions-- Further Properties of Henstock-Kurzweil Integrable Functions-- The Henstock Variational Measure-- Multipliers for the Henstock-Kurzweil Integral-- Some Selected Topics in Trigonometric Series-- Some Applications of the Henstock-Kurzweil Integral to Double Trigonometric Series.
(source: Nielsen Book Data)
The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus. (source: Nielsen Book Data)