Additive and non-additive entropies of finite measurable partitions

A geometrical representation of entropy leads to a generalization which, in special cases, reduces to the Shannon entropy and may easily be connected to the Renyi entropy. This, in two dimensions, is here called Parabolic entropy (which may further be generalized to higher dimensions). Parabolic entropy happens to be a particular case of Polynomial entropies of finite measurable partitions. Finally, some conditional entropies are defined and their properties have been studied in order to prepare a background for the study of entropy of endomorphisms etc. in ergodic theory and for proving Shannon-Wolfowitz coding theorem.