0343871 - MÚ 2011 RIV US eng J - Článek v odborném periodiku
Jech, Thomas
Algebraic characterizations of measure algebras.
Proceedings of the American Mathematical Society. Roč. 136, č. 4 (2008), s. 1285-1294. ISSN 0002-9939. E-ISSN 1088-6826
Grant CEP: GA AV ČR IAA100190509
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: Von-Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.584, rok: 2008 ; AIS: 0.689, rok: 2008

We present necessary and sufficient conditions for the existence of a countably additive measure on a Boolean sigma-algebra. For instance, a Boolean sigma-algebra B is a measure algebra if and only if B - {0} is the union of a chain of sets C-1 subset of C-2 subset of.... such that for every n, (i) every antichain in C-n has at most K(n) elements (for some integer K(n)), (ii) if {a(n)}(n) is a sequence with a(n) is not an element of C-n for each n, then lim(n) a(n) = 0, and (iii) for every k, if {a(n)} n is a sequence with limn an = 0, then for eventually all n, a(n) is not an element of C-k. The chain {Cn} is essentially unique.
Trvalý link: http://hdl.handle.net/11104/0186246