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2002/2003 Typical properties of correlation dimension.
Józef Myjak, Ryszard Rudnicki
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Real Anal. Exchange 28(2): 269-278 (2002/2003).


Let \((X,\rho)\) be a complete separable metric space and \(\mathcal M\) be the set of all probability Borel measures on \(X\). We show that if the space \(\mathcal M\) is equipped with the weak topology, the set of measures having the upper (resp. lower) correlation dimension zero is re\-si\-dual. Moreover, the upper correlation dimension of a typical (in the sense of Baire category) measure is estimated by means of the local lower entropy and local upper entropy dimensions of \(X\).


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Józef Myjak. Ryszard Rudnicki. "Typical properties of correlation dimension.." Real Anal. Exchange 28 (2) 269 - 278, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1048.37020
MathSciNet: MR2009754

Primary: 28A80
Secondary: 54E52

Keywords: dimension , measure , residual subset

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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