Elements of Mathematics: Integration II. Chapters 7-9
This volume of the new English edition of the famous series of monographs contains chapters 7, 8, and 9, which are devoted to integration theory. The first six chapters can be found in Integration I of the new English edition, which also appeared recently. Chapter 7 is an exposition of the theory of Haar measures. It contains the basic theory on locally compact groups, an abstract theory, applications and examples. Exercises conclude this as well as the other chapters. The theory of convolutions and linear representations of groups is the subject of chapter 8. Measures on Hausdorff topological spaces are investigated in the last chapter. Besides the general theory, which covers results on products, disintegration, inverse limits and tight convergence of measures, a paragraph is devoted to measures on locally convex spaces. It includes the theory of Fourier transforms, Gaussian measures, measures on Hilbert spaces, etc.
Knowledge of an undergraduate course of mathematics and of some parts of Integration I is necessary for good understanding. Some preliminary experience with concrete examples of the abstract objects under consideration may be useful as well. Due to an abstract, general and exact exposition, the textbook may also be of interest for specialists in the topic.