Measure Theory and Integration

Presented here is a detailed exposition of the general theory of measure and integration. The first half of the book demonstrates the power and efficacy of Caratheodory's method in obtaining general results in the subject most quickly and naturally. The author then establishes the need of inner measures and their importance for topological measure spaces and extension theory of measures beyond Caratheodory's approach. The lifting theorem, the capacity theory of Choquet's and topology through measure find a significant place in the exposition and their interrelations with other parts of the subject are included. Treated extensively are product measures and the Radon-Nikodym theory. Special attention is given to the motivation for each concept and to the general ideas behind most of the proofs, as well as detailed outlines of their execution. Exercises are also included.