Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 56-57). Also available via the World Wide Web.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-07-26Bitstream added on 2014-06-13T19:34:55Z : No. of bitstreams: 1 santos_ln_me_rcla_parcial.pdf: 254454 bytes, checksum: e32c8bbf83212b9a080a05b6df96f529 (MD5) Bitstreams deleted on 2015-06-25T13:00:45Z: santos_ln_me_rcla_parcial.pdf,. Added 1 bitstream(s) on 2015-06-25T13:03:12Z : No. of bitstreams: 1 000719346_20160726.pdf: 224220 bytes, checksum: 33187ebbdf2a29afe4f365dc6ce932e7 (MD5) Bitstreams deleted on 2016-07-29T12:53:55Z: 000719346_20160726.pdf,. Added 1 bitstream(s) on 2016-07-29T12:54:49Z : No. of bitstreams: 1 000719346.pdf: 949531 bytes, checksum: f249fa8a2707372138d0d3be07ff83fd (MD5) / Este trabalho apresenta resultados importantes sobre a Teoria de Integração. Inicialmente é desenvolvida uma parte sobre Teoria da Medida, necessária para introduzir a integral de Lebesgue e suas propriedades. Também é apresentada a integral de Riemann-Stieltjes. Em seguida, são demonstrados resultados importantes sobre converg ência envolvendo as integrais de Lebesgue, resultados estes que não são válidos para integrais de Riemann. Para apresentar tais temas, usa-se mais fortemente as referências [1], [2], [3] e [4] / This study presents important results on Integration of Theory. The rst of all part is developed on Measure Theory which is necessary to introduce the Lebesgue integral and its properties and we introduce. It also shows the Riemann-Stieltjes integral. Important results are proved on convergence involving the integrals of Lebesgue, which are not valid for the Riemann integral. Im order to present these themes we strongly use the references [1], [2], [3] and [4]

Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure theoretic entropy and we state and prove two very important theorems, Shannon-McMillan-Breiman theorem and the Variational Principle. Distance expanding maps and their connection with the calculation of topological pressure cover the third chapter. The fourth chapter introduces Gibbs states and the very important Perron-Frobenius Operator. The fifth chapter establishes the connection between pressure and geometry. Topological pressure is used in the calculation of Hausdorff dimensions. Finally the sixth chapter introduces the notion of conformal measures.

This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.

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This dissertation explores geometric measure theory; the first part explores a question posed by Paul Erdös -- Is there a number c > 0 such that if E is a Lebesgue measurable subset of the plane with λ²(E) (planar measure)> c, then E contains the vertices of a triangle with area equal to one? -- other related geometric questions that arise from the topic. In the second part, "we parametrize the theorems from general topology characterizing the continuous images and the homeomorphic images of the Cantor set, C" (abstract, para. 5).

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18444号 / 理博第4004号 / 新制||理||1577(附属図書館) / 31322 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 加藤 毅, 教授 堤 誉志雄, 教授 小野 薫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

No description available.

Inspired by a planar partitioning problem involving multiple unbounded chambers, this thesis investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint isoperimetric problem. In two cases, a full existence-uniqueness-regularity result is proved using a convexity technique inspired by work of Talenti. The problem studied here can be interpreted physically as the identification of the equilibrium shape of a sessile liquid drop in half-space (in the absence of gravity). This is a well-studied variational problem whose full resolution requires the use of geometric measure theory, in particular the theory of sets of finite perimeter. A crash course on the theory required for the modern statement of the equilibrium shape theorem is presented in an appendix. / Thesis / Master of Science (MSc)