Moment Estimation Inequalities Based on g Random Variable on Sugeno Measure Space

In 1974, the Japanese scholar Sugeno 1 presented a kind of typical nonadditive measure, Sugeno measure, which is an important generalization of probability measure 2–6 . As we all know, the definitions and properties of moment of random variable play an important role in probability theory 7–9 . Likewise, they are also very important for Sugenomeasure. In this paper we present the analogous definitions and properties based on gλ random variable on Sugeno measure space. Then some important moment estimation inequalities based on gλ random variable are presented and proven.