Study On FKG Inequality

FKG inequality is a correlation inequality for monotone functions which was first constructed by Fortuine,Ginibre and Kasteleyn in1971. In the following years a lot of works were inspired by this result and in2004Barbato first proved FKG inequality in a special Probabilityspace. In this paper we first construct an order in a discrete space and prove FKG inequality there;then generalize some of the propositions in paper[2]; at last we deduce a special inequality in a sublinear expectation space.