Measure, Integration and Function Spaces

This text contains a basic introduction to abstract measure theory and the Lebesgue integral. Most of the standard topics in measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.