Abstract
This paper extends the results of G. Debreu's ‘Economies with a Finite Set of Equilibria’, within the context of the finite dimensional space of economies used therein, to the case where demand functions are assumed only to be continuous and to satisfy a certain technical condition. This condition, involving the concept of approximate limit, does not even require that the function be anywhere differentiable. Our main result is that the complement of the set of economies with a finite set of equilibrium prices has Lebesgue measure zero, although it need not be closed and in fact, may very well be dense.
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