TY  - BOOK
AU  - Garling,D.J.H.
TI  - Analysis on Polish spaces and an introduction to optimal transportation
T2  - London Mathematical Society student texts
SN  - 9781108377362 (ebook)
AV  - QA611.28 .G36 2018
U1  - 514/.32 23
PY  - 2018///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Polish spaces (Mathematics)
KW  - Mathematical analysis
KW  - Transportation problems (Programming)
KW  - Topology
N1  - Title from publisher's bibliographic system (viewed on 05 Jan 2018); General topology -- Metric spaces -- Polish spaces, and compactness -- Semi-continuous functions -- Uniform spaces and topological groups -- Càdlàg functions -- Banach spaces -- Hilbert space -- The Hahn-Banach theorem -- Convex functions -- Subdifferentials and the legendre transform -- Compact convex Polish spaces -- Some fixed point theorems -- Abstract measure theory -- Further measure theory -- Borel measures -- Measures on Euclidean space -- Convergence of measures -- Introduction to Choquet theory -- Optimal transportation -- Wasserstein metrics -- Some examples
N2  - A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces of probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation, illustrating just how many of the results established earlier in the book play an essential role in the theory
UR  - https://doi.org/10.1017/9781108377362
ER  -