Infinite Iterated Function Systems: A Multivalued Approach
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 1-8
MSC: 54H25, 47H10, 47H09, 37B99.
DOI: 10.4064/ba52-1-1
Abstract
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.
