Heinonen, Juha 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. Reviewer: I.A.Rus (Cluj-Napoca) Cited in 5 ReviewsCited in 966 Documents MathOverflow Questions: How do sets with unit fractional Hausdorff measure of dimension \(>1\) look like? 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 Keywords:a priori smooth structures; covering theorems; metric measure space; Sobolev spaces; quasisymmetric maps between metric spaces PDFBibTeX XMLCite \textit{J. Heinonen}, Lectures on analysis on metric spaces. New York, NY: Springer (2001; Zbl 0985.46008) Full Text: DOI