Continuity of equilibria in spaces of Bochner and Gel'fand economies

We examine the continuity of equilibrium correspondences in infinite-dimensional settings where the commodity spaces are Banach lattices. Economies are modeled as Borel probability measures on a space of characteristics, with aggregate endowments defined via Bochner or Gel'fand integrals. Within this framework, we prove that the equilibrium correspondence is continuous on a dense subset of the domain of economies admitting equilibria, endowed with a suitable Polish topology. These results extend both classical and recent continuity theorems by providing a unified analytical treatment applicable to a substantially broader class of locally convex spaces and encompass models with infinite planning horizons, monopolistic competition, neoclassical economies, financial equilibria, and asymmetric information. Importantly, this study demonstrates that there is no necessity to impose differentiability assumptions that are typically required in regular economies to study equilibrium continuity.