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1	Lebesgue points, Hölder continuity and Sobolev functions Karlsson, John January 2009 (has links) <p>This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L<sup>1</sup> functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points.</p> Lebesgue point Hausdorff dimension Hausdorff measure Hölder continuity Maximal function Poincaré inequality Sobolev space Uniform continuity
2	Lebesgue points, Hölder continuity and Sobolev functions Karlsson, John January 2009 (has links) This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points. Lebesgue point Hausdorff dimension Hausdorff measure Hölder continuity Maximal function Poincaré inequality Sobolev space Uniform continuity
3	Coherence Spaces and Uniform Continuity / 整合空間と一様連続性 Matsumoto, Kei 23 March 2017 (has links) 京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20157号 / 理博第4242号 / 新制\|\|理\|\|1610(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授照井一成, 教授岡本久, 教授長谷川真人 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM coherence spaces linear logic uniform spaces uniform continuity realizability theory computable analysis 400
4	On some results of analysis in metric spaces and fuzzy metric spaces Aphane, Maggie 12 1900 (has links) The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics) Metric space Cauchy sequence Compactness Precompactness Completeness Continuity Uniform continuity Isometry Uniform convergence Seperable Nested Closed sets Diameter Pseudo metric space Fuzzy metric space Standard fuzzy metric space Fuzzy pseudo metric space Metric identification Fuzzy metric identification Nonexpansive map t-nonexpansive map t-uniformly continuous map t-isometry map Quotient map Quotient topology Quotient space Natural map Topological space 514.325 Metric spaces Fuzzy topology
5	On some results of analysis in metric spaces and fuzzy metric spaces Aphane, Maggie 12 1900 (has links) The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics) Metric space Cauchy sequence Compactness Precompactness Completeness Continuity Uniform continuity Isometry Uniform convergence Seperable Nested Closed sets Diameter Pseudo metric space Fuzzy metric space Standard fuzzy metric space Fuzzy pseudo metric space Metric identification Fuzzy metric identification Nonexpansive map t-nonexpansive map t-uniformly continuous map t-isometry map Quotient map Quotient topology Quotient space Natural map Topological space 514.325 Metric spaces Fuzzy topology

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