Hardcover ISBN:  9783037191583 
Product Code:  EMSILMTP/25 
List Price:  $48.00 
AMS Member Price:  $38.40 
Hardcover ISBN:  9783037191583 
Product Code:  EMSILMTP/25 
List Price:  $48.00 
AMS Member Price:  $38.40 

Book DetailsEMS IRMA Lectures in Mathematics and Theoretical PhysicsVolume: 25; 2016; 194 ppMSC: Primary 53; Secondary 28; 30; 35; 54; 58; 60
This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and NonRiemannian Spaces and based on the idea of the concentration of measure phenomenon by Lévy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions.
One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvaturedimension condition is also discussed.
A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and research mathematicians interested in metric measure spaces.

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Requests
This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and NonRiemannian Spaces and based on the idea of the concentration of measure phenomenon by Lévy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions.
One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvaturedimension condition is also discussed.
A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.
Graduate students and research mathematicians interested in metric measure spaces.