Permanence of the Donsker Property

Abstract

In this chapter we consider a number of operations that preserve the Donsker property and allow the formation of many new Donsker classes from given examples. For instance, unions, convex hulls, and certain closures of Donsker classes are Donsker. The main result of this chapter concerns Lipschitz transformations of Donsker classes and is discussed in Section 2.10.2. Section 2.10.3 covers the preservation of the uniform-entropy condition, and in Section 2.10.4 new Donsker classes are formed through union of sample spaces.