Whereas a Hilbert space is separable if and only if it admits a countable orthonormal basis, the range of a continuous random variable x is an uncountable set (i.e. the probability that the system is "at position x " will always be zero). As such, eigenstates of an observable need not necessarily be measurable functions belonging to L (X) (see normalization condition below). A typical example is the position operator x ^ ^ defined as