Naudts-like duality and the extreme Fisher information principle

We show that using Frieden and Soffer's extreme information principle [Phys . Rev. E 52, 2274 (1995)] with a Fisher measure constructed with escort pro babilities [C. Beck and F. Schlogel, Thermodynamics of Chaotic Systems (Cam bridge University Press, Cambridge, England, 1993)], the concomitant soluti ons obey a type of Naudts's duality (e-print cond-mat/990470) for nonextens ive ensembles [C. Tsallis, in Nonextensive Statistical Mechanics and its Ap plications, Lecture Notes in Physics, edited by S. Abe and Y. Okamoto (Spri nger-Verlag, Berlin, in press)].