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An Extension Theorem Concerning Frechet Measures

Published online by Cambridge University Press:  20 November 2018

Ron C. Blei
Ron C. Blei*
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
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Abstract

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An F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.

Keywords

28A3546E2726D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 278 - 285
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Blei, R., Fractional dimensions and bounded fractional forms, Mem. Amer. Math. Soc. 57(1985), 331.Google Scholar
2. Blei, R. and Kahane, J.-R, A computation of the Littlewood exponent of stochastic processes, Math. Proc. Cambridge Philos. Soc. 103(1988), 367–370.Google Scholar
3. Blei, R. and Schmerl, J., Combinatorial dimension of fractional Cartesian products, Proc. Amer. Math. Soc. 120(1994), 73–77.Google Scholar
4. Clarkson, J. A. and Adams, C. R., On definitions of bounded variation for functions of two variables, Trans. Amer. Math. Soc. 35(1933), 824–854.Google Scholar
5. Diestel, J. and Uhl, J. J., Jr., Vector Measures, Math. Surveys Monographs 15, Amer. Math. Soc, Providence, Rhode Island, 1977.Google Scholar
6. Dobrakov, I., On extension of Vector Poly measures, Czechoslovak Math. J. 38(1988), 88–94.Google Scholar
7. Dunford, N. and Schwartz, J. T., Linear Operators, I, Interscience Publishers, Inc., New York, 1964.Google Scholar
8. Fréchet, M., Sur les fonctionnelles bilinéaires, Trans. Amer. Math. Soc. 16(1915), 215–234.Google Scholar
9. Littlewood, J. E., On bounded bilinear forms in an infinite number of variables, Quart. J. Math. Oxford 1(1930), 164–174.Google Scholar
10. Morse, M. and Transue, W., C-Bimeasures and their integral extensions, Ann. of Math. 64(1956), 480–504.Google Scholar
11. Towghi, N., Stochastic integration of processes with finite generalized variations, Ann. Probab., to appear.Google Scholar
12. Ylinen, K., On vector bimeasures, Ann. Mat. Pura Appl. 117(1978), 115–138.Google Scholar