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2013 | 11 | 3 | 487-508
Tytuł artykułu

On some properties of Hamel bases and their applications to Marczewski measurable functions

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EN
Abstrakty
EN
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.
Twórcy
  • Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI, 48109-1043, USA, dorais@umich.edu
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland, rfilipow@mat.ug.edu.pl
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland, mattn@mat.ug.edu.pl
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0144-1
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