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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.
Sample Chapter(s)
Chapter 1: The one-dimensional Henstock-Kurzweil integral (233 KB)
Contents:
- 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
Readership: Graduate students and researchers in real analysis.
