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Title:Metric entropies of various function spaces
Author(s):Strus, Joseph Michael
Doctoral Committee Chair(s):Kaufman, Robert
Department / Program:Mathematics
Engineering, Electronics and Electrical
Discipline:Mathematics
Engineering, Electronics and Electrical
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Engineering, Electronics and Electrical
Abstract:The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as $\varepsilon\ \to {\rm 0}\sp{+}$ for various function spaces. Some spaces we consider are the Sobolov spaces $L\sbsp{1}{p}$((0, 1)) for 1 $<$ $p \leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).
Issue Date:1994
Type:Text
Language:English
URI:http://hdl.handle.net/2142/23623
Rights Information:Copyright 1994 Strus, Joseph Michael
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9503333
OCLC Identifier:(UMI)AAI9503333


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