What is "self-information"

In information theory, self-information or surprisal is a measure of the information content associated with an event in a probability space or with the value of a discrete random variable. It is expressed in a unit of information, for example bits, nats, or hartleys, depending on the base of the logarithm used in its calculation.

The term self-information is also sometimes used as a synonym of the related information-theoretic concept of entropy. These two meanings are not equivalent, and this article covers the first sense only.