A certain property of abelian groups
Witold Seredyński, Jacek Świątkowski (1993)
Colloquium Mathematicae
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Witold Seredyński, Jacek Świątkowski (1993)
Colloquium Mathematicae
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L. Ramsey (1996)
Colloquium Mathematicae
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Timmesfeld, Franz Georg (2003)
Beiträge zur Algebra und Geometrie
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W. Comfort, F. Trigos-Arrieta, Ta-Sun Wu (1997)
Fundamenta Mathematicae
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M. S. Audu, A. Afolabi, E. Apine (2006)
Kragujevac Journal of Mathematics
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Zelenyuk, E.G., Protasov, I.V. (2001)
Sibirskij Matematicheskij Zhurnal
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Sławomir Solecki (1996)
Fundamenta Mathematicae
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We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-locally-compact groups.) Thus we obtain the following characterization of locally compact, abelian...
Turmanov, M.A. (2001)
Sibirskij Matematicheskij Zhurnal
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Masanari Kida (1995)
Acta Arithmetica
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Chekhlov, A.R. (2001)
Sibirskij Matematicheskij Zhurnal
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Sharma, R.K., Srivastava, J.B., Khan, Manju (2007)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Edmond Granirer (1994)
Colloquium Mathematicae
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Let be the left convolution operators on with support included in F and denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that , and are as big as they can be, namely have as a quotient, where the ergodic space W contains, and at times is very big relative to . Other subspaces of are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.