Let D(A) be the space of set-indexed functions that are outer continuous with inner limits, a generalization of D[0, 1]. This paper proves a central limit theorem for triangular arrays of independent D(A) valued random variables. The limit processes are not restricted to be Gaussian, but can be...

The Brownian motion with multi-dimensional time parameter introduced by Paul Lévy can be viewed as a set-indexed Brownian process with independent increments. This is demonstrated in a way which yields a unified representation of Lévy's Brownian motion and the Brownian sheet. Lévy's Brownian...