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Hyperreal-valued probability measures approximating a real-valued measure. (English) Zbl 1385.60008

Summary: We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated – up to an infinitesimal – by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

MSC:

60B10 Convergence of probability measures
28E05 Nonstandard measure theory
03H05 Nonstandard models in mathematics
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References:

[1] Benci, V., L. Horsten, and S. Wenmackers, “Non-Archimedean probability,” Milan Journal of Mathematics , vol. 81 (2013), pp. 121-51. · Zbl 1411.60007 · doi:10.1007/s00032-012-0191-x
[2] Cutland, N. J., “Nonstandard measure theory and its applications,” Bulletin of the London Mathematical Society , vol. 15 (1983), pp. 529-89. · Zbl 0529.28009 · doi:10.1112/blms/15.6.529
[3] Henson, C. W., “On the nonstandard representation of measures,” Transactions of the American Mathematical Society , vol. 172 (1972), pp. 437-46. · Zbl 0255.28006 · doi:10.2307/1996361
[4] Krauss, P., “Representation of conditional probability measures on Boolean algebras,” Acta Mathematica Academiae Scientiarum Hungaricae , vol. 19 (1968), pp. 229-41. · Zbl 0174.49001 · doi:10.1007/BF01894506
[5] McGee, V., “Learning the impossible,” pp. 179-99 in Probability and Conditionals: Belief Revision and Rational Decision , edited by E. Eells and B. Skyrms, Cambridge University Press, Cambridge, 1994.
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