The third and last volume of this work is devoted to integration theory and the fundamentals of global analysis. Once again, emphasis is laid on a modern and clear organization, leading to a well structured and elegant theory and providing the reader with effective means for further development. Thus, for instance, the Bochner-Lebesgue integral is considered with care, since it constitutes an indispensable tool in the modern theory of partial differential equations. Similarly, there is discussion and a proof of a version of Stokes’ Theorem that makes ample allowance for the practical needs of mathematicians and theoretical physicists.
As in earlier volumes, there are many glimpses of more advanced topics, which serve to give the reader an idea of the importance and power of the theory. These prospective sections also help drill in and clarify the material presented.
Numerous examples, concrete calculations, a variety of exercises and a generous number of illustrations make this textbook a reliable guide and companion for the study of analysis.