Duistermaat J.J., Kolk J.A.C. Multidimensional Real Analysis II: Integration

Cambridge University Press, 2004. — 395 p. — ISBN13: 978-0-521-82925-0.This book, which is in two parts, provides an introduction to the theory of vectorvalued functions on Euclidean space. We focus on four main objects of study and in addition consider the interactions between these. Volume I is devoted to differentiation. Differentiable functions on Rn come first, in Chapters 1 through
3. Next, differentiable manifolds embedded in Rn are discussed, in Chapters 4 and
5. In Volume II we take up integration. Chapter 6 deals with the theory of n-dimensional integration overRn. Finally, in Chapters 7 and 8 lower-dimensional integration over submanifolds of Rn is developed; particular attention is paid to vector analysis and the theory of differential forms, which are treated independently from each other.
Generally speaking, the emphasis is on geometric aspects of analysis rather than on matters belonging to functional analysis.