AMS Chelsea Publishing 1963; 378 pp; hardcover Volume: 161 ISBN10: 0821852736 ISBN13: 9780821852736 List Price: US$53 Member Price: US$47.70 Order Code: CHEL/161.H
 By generalizing the concept of point function to that of a function ("soma" function) over a Boolean ring, Carathéodory gives in this book an elegant algebraic treatment of measure and integration. Table of Contents  Somas: 1.12 The axiomatic method; 1.37 Elementary theory of somas; 1.813 Somas as elements of a Boolean algebra; 1.1416 The main properties of the union; 1.1722 The decomposability of somas; 1.2324 The intersection of an infinite number of somas; 1.2532 Limits and bounds
 Sets of Somas: 2.3340 Sets of somas closed under a binary operation; 2.4146 Complete rings; 2.4753 Ordinal numbers of the second class; 2.5455 Hereditary sets of somas; 2.5664 Homomorphisms of rings of somas
 Place Functions: 3.6568 Finitelyvalued place functions; 3.6975 Nests of somas; 3.7679 Altering the domain of definition; 3.8088 Principal properties of the soma functions \(\alpha(X)\) and \(\beta(X)\)
 Calculation with Place Functions: 4.8994 Limit processes; 4.95106 Elementary operations on place functions; 4.107110 Uniform and absolute convergence; 4.111117 Composition of place functions; 4.118125 Homomorphisms of place functions
 Measure Functions: 5.126128 Additive and unionbounded soma functions; 5.129130 Measurability; 5.131135 Measure functions; 5.136140 The measure function on its ring of measurability; 5.141143 Sequences of measure functions and their limits; 5.144147 Transformation of measure functions by homomorphisms; 5.148153 The BorelLebesgue content
 The Integral: 6.154 Fields of place functions; Measurable place functions; 6.155162 The notion of the integral; 6.163166 Linearity of the integral and the integration of place functions of arbitrary sign; 6.167172 Comparable measure functions and the Lebesgue decomposition; 6.173175 Abstract differentials; 6.176177 The absolute continuity of two comparable measure functions; 6.178180 Transformation of the integral by means of homomorphisms
 Application of the Theory of Integration to Limit Processes: 7.181183 The theorem of Egoroff; 7.184189 Continuity of the integral as a functional; 7.190197 Convergence in the mean; 7.198205 Ergodic theory
 The Computation of Measure Functions: 8.206210 Maximal measure functions; 8.211215 The bases of an arbitrary measure function; 8.216221 Relative measurability
 Regular Measure Functions: 9.222224 The definition and principal properties of regular measure functions; 9.225229 Inner measure; 9.230235 Comparison of inner and outer measures; 9.236240 The arithmetic mean of the inner and outer measures
 Isotypic Regular Measure Functions: 10.241244 The principal properties of isotypic measure functions; 10.245248 The Jordan decomposition of completely additive soma functions; 10.249255 The difference of two isotypic regular measure functions; 10.256257 Comparable outer measures
 Content Functions: 11.258259 The definition of content functions; 11.260267 Reduced content functions and their homomorphisms; 11.268271 The Jessen infinitedimensional torus; 11.272278 The Vitali covering theorem; 11.279282 The Lebesgue integral; 11.283284 Comparable content functions; 11.285289 Linear measure
 Appendix: Somas as elements of partially ordered sets: 12.290297 A new axiom system for somas; 12.298302 The partitioning of a set into classes; 12.303304 Partially ordered sets; 12.305308 Applications to the theory of somas; 12.309312 Systems of somas that are not isomorphic to systems of subsets of a set
 Bibliography: Earlier publications by Constantin Carathéodory on the algebraization of measure and integral
 List of symbols
 Index
