Mathematical Information Source

AKA: Information Source (Mathematics).
See: Information Entropy, Mathematics, Random Variable, Alphabet (Computer Science), Stationary Distribution, Entropy Rate.

References

(Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Information_source_(mathematics) Retrieved:2018-6-24.
- 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 : [math]\displaystyle{ H\{\bold{X}\} = \lim_{n\to\infty} H(X_n | X_0, X_1, \dots, X_{n-1}) }[/math] where : [math]\displaystyle{ X_0, X_1, \dots, X_n }[/math] is the sequence of random variables defining the information source, and : [math]\displaystyle{ H(X_n | X_0, X_1, \dots, X_{n-1}) }[/math] is the conditional information entropy of the sequence of random variables. Equivalently, one has : [math]\displaystyle{ H\{\bold{X}\} = \lim_{n\to\infty} \frac{H(X_0, X_1, \dots, X_{n-1}, X_n)}{n+1}. }[/math]