A function will be said structural entropy if
In the Rényi's case, Daróczy (1963)  restructured the axioms, while in the Havrda and Charvt's case, Daróczy (1970)  presented an alternative way to characterize the entropy of degree . This is as follows:
Let , be a real valued function satisfying:
and is as given by (3.3).
The function given by (3.16) is famous as "information function of degree ".
An alternative way to characterize the entropy of degree is following the Chaundy and McLeod's (1961)  approach. This can be seen in Sharma and Taneja (1975) , and is as follows:
Let be a real valued function satisfying
for all , and
Some alternative approaches to characterize the measure (3.51) can be seen in Aczél and Daróczy (1975) , Mathai and Rathie (1975)  and Taneja (1979) .
It is worth emphasizing here that the measure (3.3), or better , satisfies some extra properties given below.
Property 3.18. We can write
Property 3.20. Let , then
Property 3.22. For all , ,, we have