超準解析
参照文献

↑  Nonstandard Analysis in Practice. Edited by Francine Diener, Marc Diener. Springer, 1995.
↑  Nonstandard Analysis, Axiomatically. By V. Vladimir Grigorevich Kanovei, Michael Reeken. Springer, 2004.
↑  Nonstandard Analysis for the Working Mathematician. Edited by Peter A. Loeb, Manfred P. H. Wolff. Springer, 2000.
↑  森毅　『[新装版]指数・対数のはなし』　東京図書、2006年、18頁。ISBN 978-4-489-00726-2
↑  斎藤正彦 『数のコスモロジー』　筑摩書房〈ちくま学芸文庫Math＆Science〉、2007年、105頁、下から6行目
↑  Non-standard Analysis. By Abraham Robinson. Princeton University Press, 1974.
↑  Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics. By Joseph W. Dauben. www.mcps.umn.edu.
1 2 3  Robinson, A.: Non-standard analysis. North-Holland Publishing Co., Amsterdam 1966.
↑  Heijting, A. (1973) Address to Professor A. Robinson. At the occasion of the Brouwer memorial lecture given by Prof. A.Robinson on the 26th April 1973. Nieuw Arch. Wisk. (3) 21, pp. 134—137.
↑  Robinson, Abraham (1996). Non-standard analysis (Revised ed.). Princeton University Press. ISBN 0-691-04490-2
↑  Curt Schmieden and Detlef Laugwitz: Eine Erweiterung der Infinitesimalrechnung, Mathematische Zeitschrift 69 (1958), 1-39
1 2  H. Jerome Keisler, Elementary Calculus: An Infinitesimal Approach. First edition 1976; 2nd edition 1986: full text of 2nd edition
1 2  Edward Nelson: Radically Elementary Probability Theory, Princeton University Press, 1987, full text
1 2  Sergio Albeverio, Jans Erik Fenstad, Raphael Høegh-Krohn, Tom Lindstrøm: Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press 1986.
↑  中村徹：「超準解析と物理学」、日本評論社、ISBN 4-535-78248-2 (1998年6月10日)
1 2  Edward Nelson: Internal Set Theory: A New Approach to Nonstandard Analysis, Bulletin of the American Mathematical Society, Vol. 83, Number 6, November 1977. A chapter on Internal Set Theory is available at https://web.math.princeton.edu/~nelson/books/1.pdf
↑  Vopěnka, P. Mathematics in the Alternative Set Theory. Teubner, Leipzig, 1979.
↑  Vieri Benci, Mauro Di Nasso, Marco Forti. The eightfold path to nonstandard analysis. In: Nigel J. Cutland, Mauro Di Nasso, David A. Ross (eds.) Nonstandard Methods and Applications in Mathematics, Cambridge University Press, 3-44 (2006)
↑  Salbany, S.; Todorov, T. Nonstandard Analysis in Point-Set Topology. Erwing Schrodinger Institute for Mathematical Physics.
↑  Chang, C. C.; Keisler, H. J. Model theory. Third edition. Studies in Logic and the Foundations of Mathematics, 73. North-Holland Publishing Co., Amsterdam, 1990. xvi+650 pp. ISBN 0-444-88054-2
↑  中村徹『超準解析とファインマン経路積分』河合文化教育研究所, 河合出版 (発売)〈数学基礎論シリーズ〉、1997年。ISBN 4879999717。
↑  中村徹「超準解析による経路積分(量子情報理論と開放系)」『数理解析研究所講究録』第982巻、京都大学数理解析研究所、1997年3月、115-125頁、CRID 1050564285511002496、hdl:2433/60916、ISSN 1880-2818。
↑  Allen Bernstein and Abraham Robinson, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific Journal of Mathematics 16:3 (1966) 421-431
↑  P. Halmos, Invariant subspaces for Polynomially Compact Operators, Pacific Journal of Mathematics, 16:3 (1966) 433-437.
↑  L. van den Dries; A.J. Wilkie (1984). “Gromov's theorem on groups of polynomial growth and elementary logic”. Journal of Algebra 89 (2):  349-374. doi:10.1016/0021-8693(84)90223-0. ISSN 0021-8693. https://doi.org/10.1016/0021-8693(84)90223-0.
↑  Manevitz, Larry M; Weinberger, Shmuel (1996). “Discrete circle actions: A note using non-standard analysis”. Israel Journal of Mathematics (Springer) 94:  147-155. doi:10.1007/BF02762701. https://doi.org/10.1007/BF02762701.  (要購読契約)
↑  Pavol Jan Zlatos (2021). “Gordon's conjectures 1 and 2: Pontryagin-van Kampen duality in the hyperfinite setting”. Journal of Logic and Analysis 13 (1). doi:10.4115/jla.2021.13.1.
↑  Pavol Jan Zlatos (2021). “Gordon's Conjecture 3: Fourier transforms in the hyperfinite setting”. Journal of Logic and Analysis 13 (7). doi:10.4115/jla.2021.13.7.
↑  Stroyan, K. D. and Luxemburg, W. A. J. Introduction to the theory of infinitesimals. New York-London, Academic Press (1976)
↑  McCord, M. C. Non-standard analysis and homology, Fundamenta Mathematicae, 74, 21-28 (1972)
↑  Zivaljevic, Rade T. Infinitesimals, Microsimplexes and Elementary Homology Theory, The American Mathematical Monthly 93(7), 540-544 (1986)
↑  S. Mardesic, J. Segal. Shape Theory: The Inverse System Approach, North-Holland, 1982.
1 2  Garavaglia, Steven. Homology with equationally compact coefficients. Fundamenta Mathematicae 100, 89-95 (1978)
↑  Korppi, Tuomas. Vanishing of derived limits of non-standard inverse systems, Topology and its Applications 157(17), 2692-2703 (2010)
↑  Mardešić, S. and Segal, J. Shape theory, North Holland, 1982
↑  Wattenberg, Frank. Nonstandard analysis and the theory of shape, Fundamenta Mathematicae 98, 41-60 (1978)
↑  T. Kamae: A simple proof of the ergodic theorem using nonstandard analysis, Israel Journal of Mathematics vol. 42, Number 4, 1982.
↑  Glenn Shafer, Vladimir Vovk, Probability and Finance: It's Only a Game!, Wiley-Interscience, 2001.
↑  Francine Diener, Marc Diener. Ducks and rivers: three existence results, in Nonstandard Analysis in Practice, Springer, 205-224 (1995)
↑  Colombeau, J. F., New Generalized Functions and Multiplication of the Distributions. North Holland, Amsterdam, 1984.
↑  Colombeau, J. F., Elementary introduction to new generalized functions. North-Holland, Amsterdam, 1985.
↑  M.Oberguggenberger, H.Vernaeve. Internal sets and internal functions in Colombeau theory, Journal of Mathematical Analysis and Applications, 341(1), 649-659 (2008)
↑  Todorov, T.D. Colombeau’s Generalized Functions and Non-Standard Analysis, in book: Bogoljub Stanković, Endre Pap, Stevan Pilipović, Vasilij S. Vladimirov, eds. Generalized Functions, Convergence Structures, and Their Applications, Springer,  1988.
↑  磯野優介『超準解析入門－超実数と無限大の数学－』数学入門公開講座テキスト、京都大学数理解析研究所、2017年、21-25頁。
↑  VieriBenci, MauroDi Nasso. Alpha-theory: An elementary axiomatics for nonstandard analysis, Expositiones Mathematicae 21(4), 355-386 (2003)
↑  Mauro Di Nasso, Isaac Goldbring, Martino Lupini. Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory, Springer, 2019
↑  Terence Tao, A nonstandard analysis proof of Szemeredi’s theorem, .
↑  Capinski M., Cutland N. J. Nonstandard Methods for Stochastic Fluid Mechanics.
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↑  Cutland, N. Loeb Measures in Practice: Recent Advances. Berlin etc.: Springer (2001)
↑  Gordon E. I., Kutateladze, S. S., and Kusraev, A. G. Infinitesimal Analysis Dordrecht, Kluwer Academic Publishers (2002)