Open-multicommutativity of some functors related to the functor of probability measures

R.Kozhan

The property of a normal functor in the category of compact Hausdorff spaces to be open-multicommutative proposed by R. Kozhan and M. Zarichnyi is investigated. A number of normal functors related to the functor of probability measures and equipped with convex structure are considered here and it is proved that the functors $cc$, $ccP$, $G_{cc}P$ and $\lambda_{cc}P$ are open-multicommutative.

1. Bergin J. On the continuity of correspondences on sets of measures with restricted marginals, Economic Theory, 13 (1999), 471--481.

2. Ditor S. Z., Eifler L. Q. Some open mapping theorems for measures, Trans. Amer. Math. Soc., 164 (1972), 287--293.

3. Jovanovic B., Rosenthal R. Anonymous sequential games, Journal of Mathematical Economics, 17 (1988), 77--87.

4. Kozhan R. V., Zarichnyi M. M. Open-multicommutativity of the probability measure functor, 2004, pre\-print.

5. Lucas R., Prescott E. Investment under uncertainty, Econometrica, 39, (1971), 659--681.

6. Mas-Colell A. On a theorem of Schmeidler, Journal of Mathematical Economics, 13 (1984), 201--206.

7. Shchepin E. V., Functors and uncountable powers of compacta, Uspekhi Mat. Nauk. 36, no.3, 3--62 (Russian).

8. Teleiko A., Zarichnyi M. Categorical Topology of Compact Hausdorf Spaces, Math. Studies Monograph Series, Volume 5, 1999.

9. Zarichnyi M. M., Correspondences of probability measures with restricted marginals revisited, pre\-print, 2003.

	Open-multicommutativity of some functors related to the functor of probability measures
Author	R.Kozhan Ivan Franko National University of Lviv
Abstract	The property of a normal functor in the category of compact Hausdorff spaces to be open-multicommutative proposed by R. Kozhan and M. Zarichnyi is investigated. A number of normal functors related to the functor of probability measures and equipped with convex structure are considered here and it is proved that the functors $cc$, $ccP$, $G_{cc}P$ and $\lambda_{cc}P$ are open-multicommutative.
Keywords	open-multicommutativity, functor, probability measure
DOI	doi:10.30970/ms.24.1.99-106
Reference	1. Bergin J. On the continuity of correspondences on sets of measures with restricted marginals, Economic Theory, 13 (1999), 471--481. 2. Ditor S. Z., Eifler L. Q. Some open mapping theorems for measures, Trans. Amer. Math. Soc., 164 (1972), 287--293. 3. Jovanovic B., Rosenthal R. Anonymous sequential games, Journal of Mathematical Economics, 17 (1988), 77--87. 4. Kozhan R. V., Zarichnyi M. M. Open-multicommutativity of the probability measure functor, 2004, pre\-print. 5. Lucas R., Prescott E. Investment under uncertainty, Econometrica, 39, (1971), 659--681. 6. Mas-Colell A. On a theorem of Schmeidler, Journal of Mathematical Economics, 13 (1984), 201--206. 7. Shchepin E. V., Functors and uncountable powers of compacta, Uspekhi Mat. Nauk. 36, no.3, 3--62 (Russian). 8. Teleiko A., Zarichnyi M. Categorical Topology of Compact Hausdorf Spaces, Math. Studies Monograph Series, Volume 5, 1999. 9. Zarichnyi M. M., Correspondences of probability measures with restricted marginals revisited, pre\-print, 2003.
Pages	99-106
Volume	24
Issue	1
Year	2005
Journal	Matematychni Studii
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