Chapters in this book

1. Frontmatter i
2. Preface v
3. Table of Contents ix
4. Introduction 1
5. A. The general problem of integration 1
6. B. Some classical topics 13
7. C. Indications of general theory 27
8. Part I: Classical theory
9. Chapter I. Grassmann algebra 35
10. Chapter II. Differential forms 58
11. Chapter III. Riemann integration theory 79
12. Chapter IV. Smooth manifolds 112
13. Part II: General theory
14. Chapter V. Abstract integration theory 151
15. Chapter VI. Some relations between chains and functions 186
16. Chapter VII. General properties of chains and cochains 207
17. Chapter VIII. Chains and cochains in open sets 231
18. Part III: Lebesgue theory
19. Chapter IX. Flat cochains and differential forms 253
20. Chapter X. Lipschitz mappings 288
21. Chapter XI. Chains and additive set functions 310
22. Appendix I. Vector and linear spaces 341
23. Appendix II. Geometric and topological preliminaries 355
24. Appendix III. Analytical preliminaries 371
25. Index of symbols 379
26. Index of terms 383