A short existence proof for correlation dimension
The subject of investigation is the correlation dimension introduced in the work of \textit{I.~Procaccia, P.~Grassberger}, and \textit{V.~G.~E.~Hentschel} [Lect. Notes Phys. 179, 212-221 (1983)] and put on a rigorous basis by \textit{Ya.~Pesin} and \textit{A.~Tempelman} [Random Comput. Dyn. 3, 137-156 (1995; Zbl 0833.60008)]. The theorem by Pesin and Tempelman that is fundamental for precise definition of the correlation dimension asserts that this dimension is given in terms of the measure of neighborhoods of the diagonal. The paper presents a short and more simple proof of this existence theorem.
scientific article; zbMATH DE number 1279388