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

被引：2

作者：

Dorais, Francois G. ^{[1
]}

Filipow, Rafal ^{[2
]}

Natkaniec, Tomasz ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2013年 / 11卷 / 03期

关键词：

Linear function; Additive function; (s)-measurable set; Marczewski measurable set; (s)-measurable function; Marczewski measurable function; The intermediate value property; Darboux function; Connectivity function; Extendable function; Covering Property Axiom; SETS;

D O I：

10.2478/s11533-012-0144-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：487 / 508

页数：22

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