Chapter 34 Equilibrium theory in infinite dimensional spaces This chapter summarizes the account of the extension of the classical general equilibrium model to an infinite dimensional setting. The classical finite dimensional theory the commodity space is the canonical finite dimensional linear space R n . By contrast there is no canonical infinite dimensional linear space. Different economic applications require models involving different infinite dimensional linear spaces. The mathematical discipline of functional analysis has already been well developed as a tool for the abstract study of linear spaces. The chapter follows the methodology of functional analysis and attacks the existence problem. Advantage of this method is that it yields general results capable of application in a wide variety of specific models. An important line of research in classical general equilibrium theory has been the relationship of the core to the set of competitive allocations. In the infinite dimensional setting an extensive body of work has been developed which centers around the infinite dimensional version of the DebreuScarf core convergence theorem.