Infinite Iterated Function Systems: A Multivalued Approach

Volume 52 / 2004

K. Leśniak Bulletin Polish Acad. Sci. Math. 52 (2004), 1-8 MSC: 54H25, 47H10, 47H09, 37B99. DOI: 10.4064/ba52-1-1


We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.


  • K. LeśniakFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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