Compact Convex Sets and Boundary Integrals

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The book explores the evolution and significance of convexity arguments in functional analysis, particularly focusing on Choquet Theory and its integral representation theorems. Initially perceived as complex, these theorems have been simplified, revealing their crucial role in various mathematical fields such as potential theory, probability, and operator theory. The text also addresses new questions arising from the interplay between convex sets and continuous affine functions, emphasizing geometric interests and practical applications in operator theory and function algebras.