In this paper we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis, and the notion of distance in topology. In particular we study the Holder norms and their relationship to the shortage function (Luenberger (1995) and the directional distance function (Chambers, Chung and Färe (1995–96)). Along this line, we provide mathematical programs to compute the Holder distance function. However, this has a perverse property that undermines its attractiveness: it fails the commensurability condition suggested by Russell (1988). Thus, we introduce a commensurable Holder distance function invariant with respect to a change in the units of measurement. Among other things we obtain some continuity result and we prove that the well known Debreu-Farrell measure is a special case of the Holder distance function.