 Observation: Note that the Hartley function unifies the concepts of entropy defined by Boltzmann \(S = k \log W\), where W is the cardinality of the set of micro states of system S, with the concept of Shannon information \(I_S(x) = - \log p(x)\). If we consider S to be a set of messages, then the probability that we select an element x from the set (i.e., get a message from S ) under uniform distribution pis \(\frac{1}{|S|}\). \(H_0(S)\) is also known as the Hartley Entropy of S. 