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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 aredoi:10.1090/s0002-9947-1975-0369648-7 fatcat:ycmbupgopnfojkfqieyee3vdky