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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 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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