On Valdivia strong version of Nikodym boundedness property

0464470 - MÚ 2018 RIV US eng J - Journal Article
Kąkol, Jerzy - López-Pellicer, M.
On Valdivia strong version of Nikodym boundedness property.
Journal of Mathematical Analysis and Applications. Roč. 446, č. 1 (2017), s. 1-17. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GF16-34860L
Institutional support: RVO:67985840
Keywords : finitely additive scalar measure * Nikodym and strong Nikodym property * increasing tree
OECD category: Pure mathematics
Impact factor: 1.138, year: 2017
http://www.sciencedirect.com/science/article/pii/S0022247X16304413

Following Schachermayer, a subset BB of an algebra AA of subsets of \omega is said to have the N-property if a BB-pointwise bounded subset M of ba(A)ba(A) is uniformly bounded on AA, where ba(A)ba(A) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on AA. Moreover BB is said to have the strong N-property if for each increasing countable covering (Bm)m(Bm)m of BB there exists BnBn which has the N-property. The classical Nikodym-Grothendieck's theorem says that each \omega-algebra SS of subsets of Omega has the N-property.
Permanent Link: http://hdl.handle.net/11104/0263323