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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-1,
author = {K. Le\'sniak},
title = {Infinite Iterated Function Systems: A Multivalued Approach},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {1-8},
zbl = {1108.47048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-1}
}
K. Leśniak. Infinite Iterated Function Systems: A Multivalued Approach. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 1-8. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-1/