TY  - BOOK
AU  - Shioya,Takashi
AU  - Shioya,Takashi
TI  - Metric Measure Geometry: Gromov’s Theory of Convergence and Concentration of Metrics and Measures 
T2  - IRMA Lectures in Mathematics and Theoretical Physics (IRMA)
SN  - 9783037196588
PY  - 2016///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential & Riemannian geometry
KW  - bicssc
KW  - Probability & statistics
KW  - Differential geometry
KW  - msc
KW  - Measure and integration
KW  - Functions of a complex variable
KW  - Probability theory and stochastic processes
N1  - Restricted to subscribers
N2  - This book studies a new theory of metric geometry on metric measure spaces, 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 due to Lévy and Milman. A central theme in this text 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 set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov–Hausdorff topology and allows 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 curvature-dimension condition is also discussed.   This book makes advanced material accessible to researchers and graduate students interested in metric measure spaces
UR  - https://doi.org/10.4171/158
UR  - http://www.ems-ph.org/img/books/shioya_mini.jpg
ER  -