Hamel bases and measurability

Nadkarni, M. G. ; Sunder, V. S. (2004) Hamel bases and measurability Mathematics Newsletter, 14 (3). pp. 1-3.

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Official URL: http://www.imsc.res.in/~sunder/mgnvss.pdf

Abstract

This is a note - set in the background of some historic comments - discussing the relationship between measurability and Hamel bases for R over Q. We explicitly note that such a basis must necessarily fail to be Borel measurable (or even 'analytic' in the sense of descriptive set theory). We also discuss some constructions in the literature which yield Hamel bases which even fail to be Lebesgue measurable, and discussan elementary construction of a Hamel basis which is Lebesgue measurable.

Item Type:Article
Source:Copyright of this article belongs to Ramanujan Mathematical Society.
ID Code:76181
Deposited On:31 Dec 2011 08:28
Last Modified:18 May 2016 19:57

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