Vector Spaces of Non-measurable Functions

Authors: García-Pacheco, Francisco¹; Seoane-Sepúlveda, Juan²

Source: Acta Mathematica Sinica, Volume 22, Number 6, November 2006 , pp. 1805-1808(4)

Publisher: Springer

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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 β for any cardinality β. Some techniques involving measure theory and density characters of Banach spaces are used.

Keywords: lineability; spaceability; non-measurable functions; density character; 28A20; 46E15

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-005-0726-y

Affiliations: 1: Email: fgarcia@math.kent.edu 2: Email: jseoane@math.kent.edu

Publication date: 2006-11-01