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Vector Spaces of Non–measurable Functions

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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.

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Authors and Affiliations

  1. Department of Mathematics, Kent State University, Kent, Ohio 44242, USA

    Francisco J. García-Pacheco & Juan B. Seoane-Sepúlveda

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  1. Francisco J. García-Pacheco
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  2. Juan B. Seoane-Sepúlveda
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Correspondence to Francisco J. García-Pacheco.

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García-Pacheco, F.J., Seoane-Sepúlveda, J.B. Vector Spaces of Non–measurable Functions. Acta Math Sinica 22, 1805–1808 (2006). https://doi.org/10.1007/s10114-005-0726-y

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  • DOI: https://doi.org/10.1007/s10114-005-0726-y

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