Hartley function

The Hartley function is a measure of uncertainty, introduced by Ralph Hartley in 1928. If a sample from a finite set A uniformly at random is picked, the information revealed after the outcome is known is given by the Hartley function

${\displaystyle H_{0}(A):=\mathrm {log} _{b}\vert A\vert ,}$

where |A| denotes the cardinality of A.

If the base of the logarithm is 2, then the unit of uncertainty is the shannon (more commonly known as bit). If it is the natural logarithm, then the unit is the nat. Hartley used a base-ten logarithm, and with this base, the unit of information is called the hartley (aka ban or dit) in his honor. It is also known as the Hartley entropy or max-entropy.