ON COMPACT CONVEX SUBSETS OF D[0, 1]

It is proved that a subset K of D[0, 1] which is convex and conditionally compact with respect to the Skorokhod topology is conditionally compact with respect to the uniform topology on D[0, 1]. Consequences of this result are indicated for limit laws for generalized random variables in D[0, 1] which use tightness of measures as a hypothesis. A characterization of the convex, conditionally compact subsets of D[0,1] is given in terms of the modulus of continuity and finitely many jump points.