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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 22, 2012

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

  • François Dorais EMAIL logo , Rafał Filipów and Tomasz Natkaniec
From the journal Open 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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Published Online: 2012-12-22
Published in Print: 2013-3-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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