Laws of large numbers for Sugeno integrals

Abstract

Appropriate forms of the law of large numbers are shown to hold when ordinary expectations are replaced by Sugeno integrals against possibility and probability measures, which are functionals with extremely poor linearity properties. The law arises by studying the convergence of the distribution of the sample mean, hence the name ‘Distributional LLN’. Analogs of the Weak and Strong LLN are derived as well for possibilistic variables.