Geometric Integration Theory

*Frontmatter, pg. i*Preface, pg. v*Table of Contents, pg. ix*Introduction, pg. 1*A. The general problem of integration, pg. 1*B. Some classical topics, pg. 13*C. Indications of general theory, pg. 27*Chapter I. Grassmann algebra, pg. 35*Chapter II. Differential forms, pg. 58*Chapter III. Riemann integration theory, pg. 79*Chapter IV. Smooth manifolds, pg. 112*Chapter V. Abstract integration theory, pg. 151*Chapter VI. Some relations between chains and functions, pg. 186*Chapter VII. General properties of chains and cochains, pg. 207*Chapter VIII. Chains and cochains in open sets, pg. 231*Chapter IX. Flat cochains and differential forms, pg. 253*Chapter X. Lipschitz mappings, pg. 288*Chapter XI. Chains and additive set functions, pg. 310*Appendix I. Vector and linear spaces, pg. 341*Appendix II. Geometric and topological preliminaries, pg. 355*Appendix III. Analytical preliminaries, pg. 371*Index of symbols, pg. 379*Index of terms, pg. 383