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

  • Research Article
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Central European Journal of Mathematics

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI, 48109-1043, USA

    François G. Dorais

  2. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland

    Rafał Filipów & Tomasz Natkaniec

Authors
  1. François G. Dorais
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  2. Rafał Filipów
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  3. Tomasz Natkaniec
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Corresponding author

Correspondence to François G. Dorais.

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Dorais, F.G., Filipów, R. & Natkaniec, T. On some properties of Hamel bases and their applications to Marczewski measurable functions. centr.eur.j.math. 11, 487–508 (2013). https://doi.org/10.2478/s11533-012-0144-1

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  • DOI: https://doi.org/10.2478/s11533-012-0144-1

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