The Hartley function is a special case of Shannon’s entropy. Each element in the sample space is associated with probability . For an element , the Hartley of the event is , which is constant over . The average over the whole sample space is thus also equal to .
The Hartley function only depends on the number of elements in a set, and hence can be viewed as a function on natural numbers. Rényi showed that the Hartley function in base 2 is the only function mapping natural numbers to real numbers that
Condition 1 says that the uncertainty of the Cartesian product of two finite sets and is the sum of uncertainties of and . Condition 2 says that a larger set has larger uncertainty.
|Date of creation||2013-03-22 14:31:41|
|Last modified on||2013-03-22 14:31:41|
|Last modified by||kshum (5987)|