Ebook: Integral Representation: Choquet Theory for Linear Operators on Function Spaces

This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.

• A new and comprehensive approach to integrals of vector- and set-valued functions with respect to operator-valued measures,
• Integral representations for linear operators on function spaces,
• An extension of Choquet theory to linear operators