Topological Measures And Weighted Radon Measures

the long version

Due to the close interplay of measure and topology, topological measure theory is a particularly intriguing part of general measure theory. Appropriately this text starts with an introductory chapter on abstract measure theory. It presupposes some familiarity with elementary measure and integration theory and furnishes the prerequisites for the subsequent detailed exposition of the theory. The results mainly concern regularity properties of topological measures. The notions of mc measures and Lc spaces turn out to be particularly useful for the study of regularity properties of weighted Radon measures, a topic that was not treated previously in the literature. Because of their specific importance a whole chapter of purely topological content is devoted to Lc spaces. Throughout the textbook, the results are accompanied and consistently discussed by examples, ranging from routine to rather involved.