Topics on Analysis in Metric Spaces

• Concise and clear coverage of analysis in metric spaces
• Based on lecture notes from the Scuola Normale
• Supplemented with exercises of varying difficulty
• Coverage of classical and recent results

Readership: Graduate students in in applied mathematics and engineering undertaking a course on analysis in metric spaces.

Luigi Ambrosio, Scuola Normale Superiore, and Paolo Tilli, Politecnico di Torino

"This book is a concise introduction to analysis in metric spaces.." - Irmina Herburt, Zentralblatt Math, Vol 1080

"The book presents a well-chosen selection of what to say to students in the field, when time is limited, with suggestions for further studies. The enjoyable expositions of the subject is supplemented by exercises of various levels." - EMS Newsletter

"... a particularly elegant and original approach." - Mathematical Reviews

1: Some preliminaries in measure theory
2: Hausdorff measures and covering theorems in metric spaces
3: Lipschitz functions in metric spaces
4: Geodesic problem and Gromov-Hausdorff convergence
5: Sobolev spaces in a metric framework
6: A quick overview on the theory of integration