## Real Analysis Exchange

### Typical properties of correlation dimension.

#### Abstract

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

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

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.rae/1184963795

Mathematical Reviews number (MathSciNet)
MR2009754

Zentralblatt MATH identifier
1048.37020

Subjects
Secondary: 54E52: Baire category, Baire spaces

Keywords
measure dimension residual subset

#### Citation

Myjak, Józef; Rudnicki, Ryszard. Typical properties of correlation dimension. Real Anal. Exchange 28 (2002), no. 2, 269--278. https://projecteuclid.org/euclid.rae/1184963795

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