Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A nonstandard functional approach to Fubini's theorem

Author: Peter A. Loeb
Journal: Proc. Amer. Math. Soc. 93 (1985), 343-346
MSC: Primary 28E10
MathSciNet review: 770550
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we use a functional approach to the integral to obtain a special case of the Keisler-Fubini theorem; the general case can be obtained with a similar proof. An immediate application is the standard Fubini theorem for products of Radon measures. Similar methods give the Weil formula for quotient groups of compact Abelian groups.

References [Enhancements On Off] (What's this?)

  • [1] A. E. Hurd and P. A. Loeb, An introduction to nonstandard real analysis, Academic Press (to appear). MR 806135 (87d:03184)
  • [2] H. J. Keisler, An infinitesimal approach to stochastic analysis, Mem. Amer. Math. Soc. No. 297 (1984). MR 732752 (86c:60086)
  • [3] P. A. Loeb, An introduction to nonstandard analysis and hyperfinite probability theory, Probabilistic Analysis and Related Topics (A. T. Bharucha-Reid, ed.), Academic Press, New York, 1979, pp. 105-142. MR 556680 (80m:60005)
  • [4] -, A functional approach to nonstandard measure theory, Proc. S. Kakutani Retirement Conf., Contemporary Math., vol. 26, Amer. Math. Soc., Providence, R. I., 1984, pp. 251-261. MR 737406 (86b:28026)
  • [5] -, Measure spaces in nonstandard models underlying standard stochastic processes. Proc. Internat. Congr. of Math. (Warsaw, 1983) (to appear).
  • [6] L. H. Loomis, An introduction to abstract harmonic analysis, Van Nostrand, Princeton, N. J., 1953. MR 0054173 (14:883c)
  • [7] A. Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 0205854 (34:5680)
  • [8] K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, Pure and Appl. Math., Vol. 72, Academic Press, New York, 1976. MR 0491163 (58:10429)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28E10

Retrieve articles in all journals with MSC: 28E10

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society