Asymptotical behavior of finite and possible discontinuous economies

We consider a finite economy in which the data are depending on an exogenous parameter and the utilities satisfy a condition, previously introduced by the authors and called sequential pseudocontinuity, weaker than sequential lower semicontinuity and than sequential upper semicontinuity. We show that the economy has a nice asymptotical behavior, that is: for any sequence (x _n ) _n of exogenous parameters converging to x _o , any convergent subsequence of a sequence of approximate competitive equilibria of converges to an exact equilibrium of .