This article is cited in 7 papers

On the question of representation of ultrafilters and their application in extension constructions

A. G. Chentsov<sup>ab

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We study ultrafilters of widely understood measurable spaces and possibilities of their application as generalized elements in the construction of attraction sets in abstract attainability problems with constraints of asymptotic nature. A class of measurable spaces is specified for which all ultrafilters including free ultrafilters (with empty intersection of all of its sets) are built constructively.

Keywords: measurable space, attraction set, ultrafilter.

UDC: 519.6

Received: 12.04.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S29–S48

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