ABSTRACT
This chapter is devoted to the concept of the integral with respect to nonadditive set functions, known as the Choquet integral. This concept of integral will be used in Chapter 7 to study the convergence in distribution of random closed sets when the nonadditive set functions are capacity functionals. However the Choquet integral is also useful in many other fields such as mathematical economics (e.g., Marinacci and Montrucchio [72]), multicriteria decision making (e.g., Grabisch et al. [42]). As such we are going to present the material in a fairly general context as well as providing some motivations.
