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On Vector Sums of Measure Zero Sets

On Vector Sums of Measure Zero Sets We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result Fund. Math. 1: 105–111, 1920 is presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On Vector Sums of Measure Zero Sets

Kharazishvili, A.
Georgian Mathematical Journal , Volume 8 (3) – Sep 1, 2001
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References (10)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2001.493
Publisher site
See Article on Publisher Site

Abstract

We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result Fund. Math. 1: 105–111, 1920 is presented.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Sep 1, 2001

Keywords: Vector sum; measure zero set; transformation group; quasi-invariant measure; nonmeasurable set; absolutely negligible set

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