Uniform algebras and measures. - Kendal, Shannon (Department of Mathematics and Applied Mathematics, 2015)
The purpose of this work is to demonstrate the vital role played by measures in the study of Uniform Algebras. Most authors in the subject of Uniform Algebras are, essentially, Functional Analysts and this emphasis is apparent in their treatment of the subject. Usually the basic Measure Theoretic assumptions are mentioned at the outset and thereafter under-played or taken for granted so that one is left with very little impression of the continuous role played by, for instance, the Borel conditions or the regularity condition, in the development of the subject. We here endeavour to present this aspect.