  A probabilistic functional of efficiency has been proposed recently in order
to implement the principle of least effort and to derive Zipf-Pareto laws with
a calculus of variation. This work is a further investigation of this
efficiency measure from mathematical point of view. We address some key
mathematical properties of this functional such as its unicity, its robustness
against small variation of probability distribution and its relationship with
inequality as well as probabilistic uncertainty. In passing, a method for
calculating non-negative continuous (differential) entropy is proposed based
upon a generalized definition of informational entropy called varentropy.
