  We study the ergodic problem for fully nonlinear operators which may be
singular or degenerate when the gradient of solutions vanishes. We prove the
convergence of both explosive solutions and solutions of Dirichlet problems for
approximating equations. We further characterize the ergodic constant as the
infimum of constants for which there exist bounded sub solutions. As
intermediate results of independent interest, we prove a priori Lipschitz
estimates depending only on the norm of the zeroth order term, and a comparison
principle for equations having no zero order terms.
