The concept of a quasimartingale, and therefore also of a function of bounded variation, is extended to processes with a regular partially ordered index set V and with values in a Banach space. We show that quasimartingales can be described by their associated measures, defined on an inverse limit space S - [Omega] containing V - [Omega], furnished with the [sigma]-algebra of the predictable sets. With the help of this measure, a Rao-Krickeberg and a Riesz decomposition is obtained, as well as a convergence theorem for quasimartingales. For a regular quasimartingale X it is proven that the spaces (S - [Omega], ) and the measures associated with X are unique up to isomorphisms. In the case V = +n we prove a duality between classical (right-) quasimartingales and left-quasimartingales.
