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Vector spaces of non-measurable functions

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García-Pacheco, F.J. and Seoane-Sepúlveda, Juan B. (2006) Vector spaces of non-measurable functions. Acta Mathematica Sinica, English Series, 22 (6). pp. 1805-1808. ISSN 1439-8516

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs10114-005-0726-y


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Abstract

We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimension beta for any cardinality beta. Some techniques involving measure theory and density characters of Banach spaces are used.


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability Non-measurable functions; Density character
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20209
Deposited On:04 Mar 2013 15:30
Last Modified:28 Nov 2016 09:34

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