by Lee Peng-Yee (National University of Singapore)

This is an introductory book on Henstock integration, otherwise known as generalized Riemann integral. It is self-contained and introductory. The author has included a series of convergence theorems for the integral, previously not available. In this book, he has also developed a technique of proof required to present the new as well as the classical results.

• The Henstock-Kurzweil Integral:
  • Introduction
  • Definition and Examples
  • Simple Properties
  • Some Convergence Theorems
  • Absolute Integrability and Measurability
• The Denjoy-Perron Integral:
  • The Denjoy Integral
  • The Perron Integral
  • The Variational Integral
  • A Riesz-Type Definition
• Riesz Representation Theorems:
  • Sargent Spaces
  • Linear Functionals
  • A Nonlinear Integral
  • THE RIEMANN-TYPE INTEGRALS: The RL Integral and the McShane Integral
  • The DL Integral
  • Numerical Integration
• Some Generations:
  • Approximately Continuous Integrals
  • The Cesaro-Perron Integral
  • The Kunugi Integral
  • A General Theory