Order preserving property of measures of information

If the amount of information contained in a r.v is greater than that contained in another r.v for one measure of information, it seems reasonable to require that this relation remains true for any other valid measure. In this paper we investigate divergence and Fisher-type measures of information with respect to this property which is due to Shiva, Ahmed and Georganas (1973). It is shown that the property is satisfied only for a certain region of values of the parameter (order) a of the measures of information.