This paper is concerned with the representation of stable autonomous discrete-time systems with quantised state measurements. It is assumed that the state space R" is partitioned into disjoint regions 2(x) which are enumerated. Only the number z(k) of the region 2(x) to which the state x(k) belongs can be measured. As a consequence, the initial state x(0) is an element of R" is unknown and assumed to be uniformly distributed over the set 2(x)(z(0)) associated with the measurement z(0). The paper shows that the measurement sequence z(k) (k = 0, 1, ...) is, in general, not a Markov chain. Hence, the sequence of probability distributions cannot be represented exactly by a stochastic automaton whose state set equals the set of measurement symbols.