과제정보
연구 과제 주관 기관 : National Natural Science Fund of China
참고문헌
- I. Ben Yaacov, On theories of random variables, Israel J. Math. 194 (2013), no. 2, 957-1012. https://doi.org/10.1007/s11856-012-0155-4
- I. Ben Yaacov, A. Berenstein, and C. W. Henson, Almost indiscernible sequences and convergence of canonical bases, J. Symb. Log. 79 (2014), no. 2, 460-484. https://doi.org/10.1017/jsl.2013.38
- I. Ben Yaacov, A. Berenstein, C. W. Henson, and A. Usvyatsov, Model theory for metric structures, in: Model theory with applications to algebra and analysis. Vol. 2, 315-427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.
- I. Ben Yaacov and A. Usvyatsov, On d-finiteness in continuous structures, Fund. Math. 194 (2007), no. 1, 67-88. https://doi.org/10.4064/fm194-1-4
- I. Ben Yaacov and A. Usvyatsov, Continuous first order logic and local stability, Trans. Amer. Math. Soc. 362 (2010), no. 10, 5213-5259. https://doi.org/10.1090/S0002-9947-10-04837-3
- A. Berenstein and C. W. Henson, Model theory of probability spaces, submitted.
- I. Berkes and H. P. Rosenthal, Almost exchangeable sequences of random variables, Z. Wahrsch. Verw. Gebiete 70 (1985), no. 4, 473-507. https://doi.org/10.1007/BF00531863
- G. Dall'Aglio, Sugli estremi dei momenti delle funzioni di ripartizione doppia, Ann. Scuoloa Norm. Sup. Pisa (3) 10 (1956), 35-74.
- R. Dudley, Probabilities and Metrics, Convergence of laws on metric spaces, with a view to statistical testing, Lecture Notes Series, No. 45, Matematisk Institut, Aarhus Universitet, Aarhus, 1976.
- D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, Volume 3, NorthHolland, 1989.
- E. H. Lieb and M. Loss, Analysis, Second Edition, Graduate Studies in Mathematics, Volume 14, American Mathematical Society, 2001.
- S. Song, Model theory and probability, Thesis, University of Illinois at Urbana-Champaign, 2011.
- S. Song, On d-finite tuples in random variable structures, Fund. Math. 221 (2013), no. 3, 221-230. https://doi.org/10.4064/fm221-3-2
- A. Szulga, On the Wasserstein metric, Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), Vol. B, 267-273, Reidel, 1978.
- S. Vallander, Calculations of the Vassersten distance between probability distributions on the line, Teor. Verojatnost. i Primenen. 18 (1973), 824-827.
- C. Villani, Optimal Transport, Old and New, Grundlehren der Mathematischen Wis-senschaften [Fundamental Principles of Mathematical Sciences], 338. Springer-Verlag, 2009.