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Analysis on Polish Spaces and an Introduction to Optimal Transportation
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    Analysis on Polish Spaces and an Introduction to Optimal Transportation
    • Online ISBN: 9781108377362
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Book description

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.

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Further Reading
[Bi I] Patrick, Billingsley, Convergence of Probability Measures, John Wiley, 1968.
[Bi II] Patrick, Billingsley, Probability and Measure, John Wiley, 1979.
[Bo] Bela, Bollobas, Linear Analysis, Cambridge Mathematical Textbooks, 1990.
[BB] H., Brezis and F.E. Browder, A General Principle on Ordered Sets in Nonlinear Functional Analysis, Advances in Mathematics 21 (1976), 355– 364.
[D] R.M., Dudley, Real Analysis and Probability, Cambridge University Press, 2005.
[Duo] Javier, Duoandikoetxea, Fourier Analysis, AMS Graduate Studies in Mathematics 29, 2001.
[E] Ivar, Ekeland, Nonconvex minimization problems, Bulletin of the American Mathematical Society (New Series) (1979), 443–474.
[GMcC] Wilfrid, Gangbo and Robert J., McCann, The Geometry of Optimal Transportation, Acta Mathematica 177 (1966), 113–161.
[G II] D.J.H., Garling, A Course in Mathematical Analysis, Volume II, Cambridge University Press, 2013.
[G III] D.J.H., Garling, A Course in Mathematical Analysis, Volume III, Cambridge University Press, 2014
[G III] D.J.H. Garling, A Course in Mathematical Analysis, Volume III, Cambridge University Press, 2014.
[H] Paul R., Halmos, Measure Theory, Van Nostrand Reinhold, 1969.
[J] I.M., James, Introduction to Uniform Spaces, L.M.S. Lecture Note Series 144 1990.
[LT] Joram, Lindenstrauss and Lior, Tzafriri, Classical Banach Spaces, Volumes I and II, Springer-Verlag, 1977 and 1979.
[Pe] Gert K., Pedersen, The Existence and Uniqueness of the Haar Integral on a Locally Compact Topological Group, Report, Preprint, University of Copenhagen, 2000.
[P I] R.R., Phelps, Convex Functions, Monotone Operators and Differentiability, Springer Lecture Notes in Mathematics 1364, 1993.
[P II] R.R., Phelps, Lecture Notes on Choquet's Theorem, Springer Lecture Notes in Mathematics 1757, 2008.
[R] R. Tyrrell, Rockafellar, Convex Analysis, Princeton University Press, 1972.
[S] Barry, Simon, Convexity: An Analytic Viewpoint, Cambridge Tracts in Mathematics 187, 2011.
[Ss] Stephen, Simons, From Hahn–Banach to Monotonicity, Springer Lecture Notes in Mathematics 1693, 2008.
[SS] Lynn Arthur, Steen and J. Arthur, Seebach, Jr., Counterexamples in Topology, Dover Publications Inc., 1995.
[V I] Cedric, Villani, Topics in Optimal Transportation, American Mathematical Society, 2003.
[V II] Cedric, Villani, Optimal Transport, Old and New, Springer-Verlag, 2009.
[W] P., Wojtaszczyk, Banach Spaces for Analysts, Cambridge Studies in Advanced Mathematics, 1991.
[Y] N.J., Young, An Introduction to Hilbert Space, Cambridge University Press, 1988.


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