Metric Measure Geometry

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 Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon by Levy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the s...