Geometric Integration Theory / / Hassler Whitney.

• Superior document: Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979
• VerfasserIn: Whitney, Hassler,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2015]; ©1957
• Year of Publication: 2015
• Language: English
• Series: Princeton Legacy Library ; 2210
• Physical Description: 1 online resource (404 p.)

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Table of Contents

Frontmatter -- Preface -- Table of Contents -- Introduction -- A. The general problem of integration -- B. Some classical topics -- C. Indications of general theory -- Part I: Classical theory -- Chapter I. Grassmann algebra -- Chapter II. Differential forms -- Chapter III. Riemann integration theory -- Chapter IV. Smooth manifolds -- Part II: General theory -- Chapter V. Abstract integration theory -- Chapter VI. Some relations between chains and functions -- Chapter VII. General properties of chains and cochains -- Chapter VIII. Chains and cochains in open sets -- Part III: Lebesgue theory -- Chapter IX. Flat cochains and differential forms -- Chapter X. Lipschitz mappings -- Chapter XI. Chains and additive set functions -- Appendix I. Vector and linear spaces -- Appendix II. Geometric and topological preliminaries -- Appendix III. Analytical preliminaries -- Index of symbols -- Index of terms