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Conversion from nonstandard to standard measure spaces and applications in probability theory. (English) Zbl 0312.28004

MSC:
28A10 Real- or complex-valued set functions
60A05 Axioms; other general questions in probability
60J99 Markov processes
03H99 Nonstandard models
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[1] Allen R. Bernstein and Peter A. Loeb, A non-standard integration theory for unbounded functions, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Springer, Berlin, 1974, pp. 40 – 49. Lecture Notes in Math., Vol. 369.
[2] William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York; Chapman and Hall, Ltd., London, 1957. 2nd ed. · Zbl 0077.12201
[3] Paul G. Hoel, Sidney C. Port, and Charles J. Stone, Introduction to statistical theory, Houghton Mifflin Co., Boston, Mass., 1971. The Houghton Mifflin Series in Statistics. Paul G. Hoel, Sidney C. Port, and Charles J. Stone, Introduction to stochastic processes, Houghton Mifflin Co., Boston, Mass., 1972. The Houghton Mifflin Series in Statistics. Paul G. Hoel, Sidney C. Port, and Charles J. Stone, Introduction to probability theory, Houghton Mifflin Co., Boston, Mass., 1971. The Houghton Mifflin Series in Statistics. · Zbl 0265.62001
[4] Peter A. Loeb, A non-standard representation of measurable spaces, \?_\infty , and \?*_\infty , Contributions to non-standard analysis (Sympos., Oberwolfach, 1970), North-Holland, Amsterdam, 1972, pp. 65 – 80. Studies in Logic and Found. Math., Vol. 69.
[5] Peter A. Loeb, A nonstandard representation of Borel measures and \?-finite measures, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Springer, Berlin, 1974, pp. 144 – 152. Lecture Notes in Math., Vol. 369.
[6] W. A. J. Luxemburg, A general theory of monads, Applications of Model Theory to Algebra, Analysis, and Probability (Inte rnat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 18 – 86.
[7] Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. · Zbl 0102.00708
[8] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. · Zbl 0121.05501
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