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Lectures on analysis on metric spaces. (English) Zbl 0985.46008
Universitext. New York, NY: Springer. x, 140 p. DM 79.00; öS 577.00; sFr. 70.00; £27.00; $ 34.95 (2001).
This book is written as a graduate course on analysis in the spaces with no a priori smooth structures (basic covering theorems and their applications to analysis in metric measure space, Sobolev spaces, quasisymmetric maps between metric spaces). It is a very well written book. Much of the material is relatively recent and appears for the first time in book format. The list of references is impressive. So, it is a very recommendable book for all who are interested in analysis on metric spaces.

MSC:
46Exx Linear function spaces and their duals
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
46G05 Derivatives of functions in infinite-dimensional spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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