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Series in Real Analysis - Vol. 2
LANZHOU LECTURES ON HENSTOCK INTEGRATION
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.
Contents:
- The Henstock-Kurzweil Integral:
- Introduction
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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
Readership: Mathematicians.
| 192pp |
Pub. date: May 1989 |
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