THE REPRESENTATION OF COMPOSITION STRUCTURES

A composition structure is a sequence of consistent probability distri butions for compositions(ordered partitions) of n = 1, 2,.... Any comp osition structure can be associated with an exchangeable random compos ition of the set of natural numbers. Following Donnelly and Joyce, we study the problem of characterizing a generic composition structure as a convex mixture of the ''extreme'' ones. We topologize the family u of open subsets of [0, 1] so that u becomes compact and show that u is homeomorphic to the set of extreme composition structures. The genera l composition structure is related to a random element of u via a cons truction introduced by J. Pitman.