A moment coboundary theorem for C[0,1]-valued random fields

K. Schmidt (1977) proved that if a strictly stationary sequence of real-valued random variables has the property that the family of distributions of its partial sums is tight, then the sequence is a coboundary, meaning that it is equal to the successive differences of another strictly stationary sequence. The result here is a coboundary-type theorem for C[0,1]-valued random fields (not necessarily stationary) that includes moment conditions.