## Abstract

This article is a part of the theory developed by the author in which the following problem is solved under natural assumptions: to find necessary and sufficient conditions under which the union of at most countable family of algebras on a certain set X is equal to (Formula presented.). Here the following new result is proved. Let (Formula presented.) be a finite collection of algebras of sets given on a set X with (Formula presented.), and for each λ there exist at least (Formula presented.) pairwise disjoint sets belonging to (Formula presented.). Then there exists a family (Formula presented.) of pairwise disjoint subsets of (Formula presented.) except the case (Formula presented.); and for each λ the following holds: if (Formula presented.) and Q contains one of the two sets (Formula presented.), and its intersection with the other set is empty, then (Formula presented.).

Original language | English |
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Journal | Journal of Inequalities and Applications |

Volume | 2015 |

Issue number | 1 |

DOIs | |

State | Published - 1 Dec 2015 |

## Keywords

- algebra of sets
- pairwise disjoint sets
- ultrafilter
- σ-algebra

## All Science Journal Classification (ASJC) codes

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics