Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T16:25:14.075Z Has data issue: false hasContentIssue false
  • English
  • Français

No b-concentrated measures whenever 1<b≤2

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

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

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.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 37 - 41
Copyright
Copyright © University College London 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Buczolich, Z. and Laczkovich, M.. Concentrated Borel Measures. Ada Math. Hung., 57 (1991), 349–362.CrossRefGoogle Scholar
2.Buczolich, Z.. No concentrated measures withb’ 1.01. Real Analysis Exchange, 18 (1993–94), 612–615.CrossRefGoogle Scholar
3.Plewik, S.. No b–concentrated measures whenever bnk(bn- 1) = 1, Ada Math. Hung., 71 (1996), 211–214.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