Product Measure And Convergence Properties Of Generalized Pairwise NQD Random Sequences

We study the following 2 question:l.A Property on Product Measure;2.Convergence Properties of Generalized Pairwise NQD Random Sequences.Question 1 is discussed in chapter 2,The positive corretativeproperty of two L²-integrable random variables has been studied by many papers.For example,the inequality FKG discussed the positive corretative property of twoL²-integrable in-creasing random variables.In chapter 2,we discussed the positive corretative prop-erty on L₂(R^N,P),that is:Let N be nature number and {μ_n}_n^∞=1 be forall probability measure sequence on R¹.Set P=(?)_μn.If f and g belong to L²(R^N,P) and f(x₁,x₂,...,x_n,... ),g(x₁,x₂...,x_n,...) are increasing functions about every x_n on Rⁿ.(x₁,.x₂,...,x_n,...) stands for a point in R^N,then the following positive correlative property is ture:∫_R^Nfgdp≥∫_R^Nfdp∫_R^NgdpIn 1966 the famous statistic Lehmann gived the definition of Pairwise NQD Random Sequence,and got many relative propertis and theorems.In the definition of Pairwise NQD Random Sequence,there has the condition:P(Z＜x,Y＜y)≤P(X＜x)P(Y＜y),In reality,many random variables don't satisify the condition,but belong to the case:P(Z＜z,Y＜y)≤cP(Z＜z)P(Y＜y),and P(X＞x,Y＞y)≤cP(X＞x)P(Y＞y)(c≥1). This belong to generalized random variable sequence.Pairwise NQD Random Se-quences is the special case of Generalized Pairwise NQD Random Sequences.So it is very important in application.This is the question 2.