Geodesic
On one example of representing the ultrafilter space for an algebra of sets
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 293-311

Voir la notice de l'article provenant de la source Math-Net.Ru

Abstract problems on attainability with constraints of asymptotic nature often involve a situation when the class of sequential approximate sequence solutions (which corresponds conceptually to Vargas approach in control theory problems) is insufficient for the reproduction of effects related to the realization of limit states corresponding to the observance of asymptotic constraints. In this situation, it is necessary to use filters or nets in the original space of solutions. In the case of using filters, as easily seen, it is sufficient to take ultrafilters as analogs of Vargas approximate solutions. However, free ultrafilters, which are the most interesting form this point of view variants of ultrafilters, do not admit a constructive description. The situation can be corrected in some cases of using ultrafilters of an algebra of sets, which turns out to be acceptable in some problems of the above type. In this context, classes of measurable spaces with algebras (or, which is practically the same, with semialgebras) of sets are of interest, as they can be used to describe the set of all free ultrafilters. We analyze an example of this kind and discuss some general constructions related to representations of the space of ultrafilters.
Keywords: algebra of sets, ultrafilter. 
@article{TIMM_2011_17_4_a26,
     author = {A. G. Chentsov},
     title = {On one example of representing the ultrafilter space for an algebra of sets},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {293--311},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a26/}
}
TY  - JOUR
AU  - A. G. Chentsov
TI  - On one example of representing the ultrafilter space for an algebra of sets
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2011
SP  - 293
EP  - 311
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a26/
LA  - ru
ID  - TIMM_2011_17_4_a26
ER  - 
%0 Journal Article
%A A. G. Chentsov
%T On one example of representing the ultrafilter space for an algebra of sets
%J Trudy Instituta matematiki i mehaniki
%D 2011
%P 293-311
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a26/
%G ru
%F TIMM_2011_17_4_a26
A. G. Chentsov. On one example of representing the ultrafilter space for an algebra of sets. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 293-311. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a26/