Umfang:
1 Online-Ressource (ix, 348 Seiten)
,
Illustrationen
ISBN:
9781108377362
Serie:
London Mathematical Society student texts 89
Inhalt:
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
Inhalt:
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
Anmerkung:
Literaturverzeichnis: Seite 339-341
Weitere Ausg.:
ISBN 9781108421577
Weitere Ausg.:
ISBN 9781108431767
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Garling, David J. H., 1937 - Analysis on Polish spaces and an introduction to optimal transportation Cambridge, United Kingdom : Cambridge University Press, 2018 ISBN 9781108431767
Weitere Ausg.:
ISBN 9781108421577
Weitere Ausg.:
ISBN 1108431763
Sprache:
Englisch
Schlagwort(e):
Polnischer Raum
;
Transportproblem
DOI:
10.1017/9781108377362
URL:
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