Integral Representation Theory Applications to Convexity, Banach Spaces and Potential Theory

"This monograph provides an extensive and largely self-contained exposition of integral representation theory with emphasis on applications in mathematical analysis. It is focused on the Choquet theory of function spaces, function cones and compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time." --Book Jacket.