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On Valdivia strong version of Nikodym boundedness property

  1. 1. 0464470 - MU-W 2018 RIV US eng J - Článek v odborném periodiku
    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
    Grant CEP: GA ČR GF16-34860L
    Institucionální podpora: RVO:67985840
    Klíčová slova: finitely additive scalar measure * Nikodym and strong Nikodym property * increasing tree
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 1.138, rok: 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.
    Trvalý link: http://hdl.handle.net/11104/0263323
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