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Metric entropies of various function spaces

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Title: Metric entropies of various function spaces
Author(s): Strus, Joseph Michael
Doctoral Committee Chair(s): Kaufman, Robert
Department / Program: MathematicsEngineering, Electronics and Electrical
Discipline: MathematicsEngineering, 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
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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