Some basic properties of the set-valued measure and the defination of setvalued measure integration are given,also we discuss the convergence of set-valued measures integration.

The equiualent conditions for a bounded closed convex set-valued mapping to be a perfet additive Set-valued measure are given.

The notion of integrals scalar valued functions with respect to a set valued measure is introduced.

In this paper, first, we study the set valued measures generated by set valued increasing functions A(t), t∈R+, on product measurable space，β(R+).

On the basis of the definitions about the integrals of real measurable functions about set valued measures,the Radon Nikodym theorem of set valued measures is discussed by means of the support functions on the set valued measures,and the Radon Nikodym theorem of the classical measures is extended.

this paper makes use of some basic results of continuous parameter set valued reqular martingles and set valued measures, and gives out the relation theorems between them.

Set up Orlicz Pettis theorem under set valued condition for the first time,thus solved the problem of strong additive problem of set valued measurment and the safficient and necessary condition of weak countable and additive of set valued set function;provided the convex theorem of set valued measurement under the condition of set valued measurement σ bounded variation.

Set-valued Measures Induced by Set-valued L~1 Martingale in the Limit

Let(X,·) be a real separable Banach space with the dual X*,and(Ω,F,P) an complete probability space,further,{An,n≥1} a increase sub σ-fields filtration of F,as well as A∞=∨n≥1An,the properties of set-valued Pramart,and set-valued measures induced by set-valued Pramart are discussed.