A random variable is a measurable function from a probability space 
into a measurable space 
known as the state
space (Doob 1996). Papoulis (1984, p. 88) gives the slightly different definition
of a random variable 
as a real function whose domain
is the probability space 
and such that:
1. The set 
is an event for any real
number 
.
2. The probability of the events 
and 
equals zero.
The abbreviation "r.v." is sometimes used to denote a random variable.
