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The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set

The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set We prove that there exist two absolutely negligible subsets A and B of the real line R , whose algebraic sum A + B is an absolutely nonmeasurable subset of R . We also obtain some generalization of this result and formulate a relative open problem for uncountable commutative groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set

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References (7)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2005.455
Publisher site
See Article on Publisher Site

Abstract

We prove that there exist two absolutely negligible subsets A and B of the real line R , whose algebraic sum A + B is an absolutely nonmeasurable subset of R . We also obtain some generalization of this result and formulate a relative open problem for uncountable commutative groups.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Sep 1, 2005

Keywords: Invariant measure; quasi-invariant measure; absolutely negligible set; absolutely nonmeasurable set; extension of measure

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