Buch, Englisch, Band 109, 324 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 678 g
Local Geometric Theory
Buch, Englisch, Band 109, 324 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 678 g
Reihe: Cambridge Tracts in Mathematics
ISBN: 978-0-521-44035-6
Verlag: Cambridge University Press
This book presents a detailed and mostly elementary exposition of the generalised 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. Defining the Lebesgue integral in Euclidean spaces from the McShane point of view has a clear pedagogical advantage: the initial stages of development are both conceptually and technically simpler. The McShane integral evolves naturally from the initial ideas about integration taught in basic calculus courses. The difficult transition from subdividing the domain to subdividing the range, intrinsic to the Lebeque definition, is completely bypassed. The unintuitive Caratheodory concept of measurability is also made more palatable by means of locally fine partitions. Although written as a monograph, the book can be used as a graduate text, and certain portions of it can be presented even to advanced undergraduate students with a working knowledge of limits, continuity and differentiation on the real line.
Autoren/Hrsg.
Weitere Infos & Material
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.
