Geodesic
Infinite Iterated Function Systems: A Multivalued Approach
K. Leśniak1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 1-8

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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.
DOI : 10.4064/ba52-1-1
Keywords: prove compact family bounded condensing multifunctions has bounded condensing set theoretic union compactness understood sense chebyshev uniform semimetric induced hausdorff distance condensity taken hausdorff measure noncompactness tool present estimate measure infinite union apply result infinite iterated function systems

K. Leśniak 1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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K. Leśniak. Infinite Iterated Function Systems:
 A Multivalued Approach. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 1-8. doi: 10.4064/ba52-1-1

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