A random variable is a measurable function from a probability space (S, S, P) into a measurable space (S', S') known as the state space. Papoulis gives the slightly different definition of a random variable X as a real function whose domain is the probability space S and such that: 1. The set {X<=x} is an event for any real number x. 2. The probability of the events {X = + ∞} and {X = - ∞} equals zero. The abbreviation "r.v." is sometimes used to denote a random variable.

principle of insufficient reason | probability space | random distribution | random number | random variate | state space | variate