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No b-concentrated measures whenever 1<b≤2

Published online by Cambridge University Press:  26 February 2010

Gábor Drasny
Affiliation:
Eötvös Loránd University, Cardiff University of Wales, MÜzeum Krt, 6–8, H-1088 Budapest, Hungary.
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Abstract

In the present paper we show that a non-zero, continuous, locally finite Borel measure on R cannot be b-concentrated for any 1 <b≤2.

Type
Research Article
Copyright
Copyright © University College London 1998

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References

1.Buczolich, Z. and Laczkovich, M.. Concentrated Borel Measures. Ada Math. Hung., 57 (1991), 349362.CrossRefGoogle Scholar
2.Buczolich, Z.. No concentrated measures withb’ 1.01. Real Analysis Exchange, 18 (1993–94), 612615.CrossRefGoogle Scholar
3.Plewik, S.. No b–concentrated measures whenever bnk(bn- 1) = 1, Ada Math. Hung., 71 (1996), 211214.CrossRefGoogle Scholar
4.Thomson, B. S.. Symmetric Properties of Real Functions. Monographs and textbooks in pure and applied mathematics, No. 183 (Marcel Dekker, New York, 1994).Google Scholar
5.Pólya, G. and Szegö, G.. Problems and Theorems in Analysis (Springer-Verlag, Berlin, 1976).CrossRefGoogle Scholar