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Riemann Approach to Integration: Local Geometric Theoryby Washek F. Pfeffer
Synopses & Reviews
This book presents a detailed and mostly elementary exposition of the generalized Riemann-Stieltjes integrals discovered by Henstock, Kurzweil, and McShane. Along with the classical results, it contains some recent developments connected with lipeomorphic change of variables and the divergence theorem for discontinuously differentiable vector fields.
A detailed exposition of generalised Riemann — Stieltjes integrals.
A detailed exposition of generalised Riemann?Stieltjes integrals.
Includes bibliographical references (p. -295) and index.
Table of Contents
Preface; Acknowledgments; Part I. One-Dimensional Integration: 1. Preliminaries; 2. The McShane integral; 3. Measure and measurability; 4. Integrable functions; 5. Descriptive definition; 6. The Henstock-Kurzweil integral; Part II. Multi-Dimensional Integration: 7. Preliminaries; 8. The McShane integral; 9. Descriptive definition; 10. Change of variables; 11. The gage integral; 12. The F-integral; 13. Recent developments; Bibliography; List of symbols; Index.
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