Several Measurable Selection Theorems on the Topological Spaces

Abstract:

      The main theorems of this paper establishes the existence of measurable selections for compact valued maps whose range space is a topological space. With the help of the measurable selection theorems, we proved the function v(ω)=sup {φ (ω, x) |x∈F(ω)} is a measurable function and the existence of measurable solution in some stochastic programmings .