Real Analysis Exchange

Typical properties of correlation dimension.

Józef Myjak and Ryszard Rudnicki

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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 \(X\).

Article information

Real Anal. Exchange, Volume 28, Number 2 (2002), 269-278.

First available in Project Euclid: 20 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A80: Fractals [See also 37Fxx]
Secondary: 54E52: Baire category, Baire spaces

measure dimension residual subset


Myjak, Józef; Rudnicki, Ryszard. Typical properties of correlation dimension. Real Anal. Exchange 28 (2002), no. 2, 269--278.

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