# Information source (mathematics)

In mathematics, an information source is a sequence of random variables ranging over a finite alphabet Γ, having a stationary distribution.

The uncertainty, or entropy rate, of an information source is defined as

$H\{\bold{X}\} = \lim_{n\to\infty} H(X_n | X_0, X_1, \dots, X_{n-1})$

where

$X_0, X_1, \dots, X_n\,$

is the sequence of random variables defining the information source, and

$H(X_n | X_0, X_1, \dots, X_{n-1})$

is the conditional information entropy of the sequence of random variables. Equivalently, one has

$H\{\bold{X}\} = \lim_{n\to\infty} \frac{H(X_0, X_1, \dots, X_{n-1}, X_n)}{n+1}.$