, Volume 11, Issue 3, pp 487-508
Date: 16 Nov 2012

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

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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.