Necessary and sufficient condition for stability of generalized   expectation value
  A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution. 
Aziz El Kaabouchi (ISMANS, France) and Sumiyoshi Abe (Mie University,   Japan and ISMANS, France)
cond-mat.stat-mech