On the Question of Representation of Ultrafilters in a Product of Measurable Spaces / Chentsov A. G. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2014. - V. 284, l. 1. - P. S65-S78.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

We study representations of ultrafilters of broadly understood measurable spaces that are realized by means of generalized Cartesian products. The structure of the arising ultrafilter space is established; in more traditional measurable spaces, this structure reduces to the realization of a Stone compact space in the form of a Tychonoff product. The developed methods can be applied to the construction of extensions of abstract reachability problems with constraints of asymptotic nature; in such extensions, ultrafilters can be used as generalized elements, which admits a conceptual analogy with the Stone-Cech compactification. The proposed implementation includes the possibility of using measurable spaces, for which the set of free ultrafilters can be described completely. This yields an exhaustive representation of the corresponding Stone compact space for measurable spaces with algebras of sets. The present issue is devoted to I.I. Eremin's jubilee; the author had many discussion with him on very different topics related to mathematical investigations, and the discussions inevitably led to a deeper understanding of their essence. The author appreciates the possibility of such communication and is grateful to Eremin, who contributed significantly to the development of the mathematical science and education in the Urals.

Author keywords:

measurable space; Tychonoff product; ultrafilter

DOI:

10.1134/S0081543814020060

Web of Science ID:

ISI:000334277400006

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	chentsov@imm.uran.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}12-01-00537-a, 13-01-90414\_ukr\_f\_a]; Programs for Fundamental Research of the Presidium of the Russian Academy of Sciences {[}12-P-1-1012, 12-P-1-1019]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 12-01-00537-a, 13-01-90414\_ukr\_f\_a), by Programs for Fundamental Research of the Presidium of the Russian Academy of Sciences (project nos. 12-P-1-1012 and 12-P-1-1019), and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013).
Number-of-Cited-References	24
Usage-Count-Since-2013	6
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	AE8UG