Measures Related to the Ball Algebra
This chapter deals with two types of topics. The material of Sections 9.2 and 9.3 is function-theoretic. The measures that are discussed there are intimately related to the holomorphic functions in B. On the other hand, Sections 9.4 and 9.5 describe some measure-theoretic aspects of the theory of function algebras in general. These would not become any simpler by specializing to the ball algebra. Both aspects are used in the proof of the Cole-Range theorem (Section 9.6), which is one of several modern generalizations of the classical theorem of F. and M. Riesz.
KeywordsBanach Space Probability Measure Toeplitz Operator Function Algebra Compact Hausdorff Space
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