In this article two problems have been contemplated. First, the R-norm entropy of a probability distribution is considered as the weighted arithmetic mean representation of elementary R-norm entropies of the occurrence of various single events. These elementary entropies are characterized using some postulates. The approach we adopted, seems to be more intuitive and elegant than that of Boekee and Lubbe (1980).On the other hand, an axiomatic characterization of R-norm inaccuracy associated with a pair of complete probability distributions P and Q, having the same number of components, is given by assuming a simple and tractable set of axioms.