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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
    • Book DOI: https://doi.org/10.1017/9781108377362
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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.

Reviews

'This book provides a detailed and concise account of analysis and measure theory on Polish spaces, including results about probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in analysis.'

Luca Granieri Source: Mathematical Reviews

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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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