ABSTRACT. The theory of measures in a topological space, as developed by V. S. Varadarajan for the algebra C of bounded continuous functions on a completely regular topological space, is extended to the context of an arbitrary uniformly closed algebra A of bounded real-valued functions. Necessary and sufficient conditions are given for A * to be represented in the natural way by a space of regular finitely-additive set functions. The concepts of additivity and tightness for these set functions are considered and some remarks about weak convergence are made.

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