Abstract
In their important (but often overlooked) paper [1]. C. Ward Henson and Frank Wallenberg introduced the notion of S-measurability. and showed that S-measurable functions are “approximately standard” (in a sense made precise in the next section).
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References
C. Ward Henson and Frank Wattenberg, “Egoroff’s theorem and the distribution of standard points in a nonstandard model”, Proc. Amer. Math. Soc., 81 (1981) 455–461.
W. A. J. Luxemburg, On some concurrent binary relations occurring in analysis, in Contributions to non-standard analysis (Sympos., Oberwolfach, 1970), Studies in Logic and Found. Math., Vol. 69, North-Holland, Amsterdam, 1972.
David A. Ross, Nonstandard measure constructions — solutions and problems, in Nonstandard methods and applications in mathematics, Lecture Notes in Logic, 25, A.K. Peters, 2006.
David A. Ross, Loeb measure and probability, in Nonstandard analysis (Edinburgh, 1996), NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., vol. 493, Kluwer Acad. Publ., Dordrecht, 1997.
David Williams, Probability with martingales, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1991.
Beate Zimmer, “A unifying Radon-Nikodým theorem through nonstandard hulls”, Illinois Journal of Mathematics, 49 (2005) 873–883.
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© 2007 Springer-Verlag Wien
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Ross, D.A. (2007). More on S-measures. In: van den Berg, I., Neves, V. (eds) The Strength of Nonstandard Analysis. Springer, Vienna. https://doi.org/10.1007/978-3-211-49905-4_15
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DOI: https://doi.org/10.1007/978-3-211-49905-4_15
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