Some important inequalities and their application on Sugeno measure space

The problem of estimating functions on the basis of indirect measurements is a universal problem of Statistical Learning Theory. In this paper, some important inequalities on Sugeno measure space are presented and proven, such as Hölder's inequality, Minkowski inequality, and Jensen's inequality. Furthermore, a useful theorem about the problem of estimating functions on the basis of indirect measurements on Sugeno measure space is given and proven by using Minkowski inequality and Jensen's inequality.