On the representation of continuous parameter processes by a sequence of random variables

This paper examines the question of representing a continuous parameter random process\{ x_t, t ∈ T \}by a sequence of random variables "without loss of information." The principal result is that such a representation by expansion coefficients relative to a basis\{ φ_i \}ofL_2(T)is always possible, regardless of the orthogonality of\{ φ_i \}and of the boundedness of the time intervalT, provided only that the process is continuous in probability and almost every sample path has finite energy.