Determining the form of the mean of a stochastic process

Let [mu] be the mean function of an observable stochastic process whose sample paths fall in some Banach space with a basis and assume [mu] is also in this space. A procedure like Cover's (Ann. Statist.1, 862-871, 1973) is given which has the property that if the last nonzero coordinate of [mu] is the mth then with probability one this is discovered after at most a finite number of erros. If [mu] has an infinite number of nonzero coordinates, then with probability one this is discovered after at most a finite number of errors except for a set of [mu] of prior probability zero.