  In this paper, the Neyman-Pearson lemma for general sublinear expectations is
studied. We weaken the assumptions for sublinear expectations in [1] and give a
completely new method to study this problem. Applying Mazur-Orlicz Theorem and
the decomposition theorem of finitely additive set functions, we prove that the
optimal test still has the reminiscent form as in the classical Neyman-Pearson
lemma. Finally, for the special sublinear expectation which can be represented
by a family of probability measures, we give a sufficient condition for the
existence of the optimal test and show the form of the optimal test selected in
L_{c}^1-space which is introduced by Peng [10] in his nonlinear-expectation
framework.
