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11	Measurable functions and Lebesgue integration Brooks, Hannalie Helena 11 1900 (has links) In this thesis we shall examine the role of measurerability in the theory of Lebesgue Integration. This shall be done in the context of the real line where we define the notion of an integral of a bounded real-valued function over a set of bounded outer measure without a prior assumption of measurability concerning the function and the domain of integration. / Mathematical Sciences / M. Sc. (Mathematics) Lebesgue integral Measurable set Outer measure Inner measure Generalised Lebesgue Integral Inner integrals Outer integrals Integrability Limit theorems Role of measurability 515.43 Lebesgue integral Measure theory Limit theorems (Probability theory)
12	Measurable functions and Lebesgue integration Brooks, Hannalie Helena 11 1900 (has links) In this thesis we shall examine the role of measurerability in the theory of Lebesgue Integration. This shall be done in the context of the real line where we define the notion of an integral of a bounded real-valued function over a set of bounded outer measure without a prior assumption of measurability concerning the function and the domain of integration. / Mathematical Sciences / M. Sc. (Mathematics) Lebesgue integral Measurable set Outer measure Inner measure Generalised Lebesgue Integral Inner integrals Outer integrals Integrability Limit theorems Role of measurability 515.43 Lebesgue integral Measure theory Limit theorems (Probability theory)
13	On the Lebesgue Integral Kastine, Jeremiah D 18 March 2011 (has links) We look from a new point of view at the definition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Hausdorff spaces. We use mini sums to give all of them a unified treatment that is more efficient than the standard ones. We also give Fubini's theorem a proof that is nicer and uses much lighter technical baggage than the usual treatments. Lebesgue measure Lebesgue integral Fubini's theorem Locally compact Hausdorff space Riesz representation theorem Mathematics
14	Tempo mÃdio de saÃda e desigualdades isoperimÃtricas para subvariedades mÃnimas de N x R / Mean exit time and isoperimetric inequalities for minimal submanifolds of N x R Francisco Pereira Chaves 24 February 2011 (has links) CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / FundaÃÃo de Amparo Ã Pesquisa do Estado do CearÃ / Estabelece desigualdades isoperimÃtricas e estimativas do tempo mÃdio de saÃda para subvariedades mÃnimas de N x R, onde N Ã uma variedade riemanniana completa com curvatura seccional nÃo-positiva. Prova desigualdades isoperimÃtricas para subvariedades com segunda forma fundamental dominada em espaÃos de Hadamard com curvatura seccional limitada. / It establishes isoperimetric inequalities and exit mean time estimates for minimal submanifolds of N x R, where N is a complete Riemannian manifold with sectional curvature non-positive. It proves isoperimetric inequalities for submanifolds with tamed second fundamental form in Hadamard spaces with bounded sectional curvature. variedades riemanianas autovalores Lebesgue, integrais de Riemannian manifolds eigenvalues Lebesgue integral GEOMETRIA DIFERENCIAL

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