{"id":78890,"date":"2006-01-03T00:00:00","date_gmt":"2006-01-03T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/integracion-en-espacios-de-banach\/"},"modified":"2006-01-03T00:00:00","modified_gmt":"2006-01-03T00:00:00","slug":"integracion-en-espacios-de-banach","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/integracion-en-espacios-de-banach\/","title":{"rendered":"Integraci\u00f3n en espacios de banach"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jose Rodriguez Ruiz <\/strong><\/h2>\n<p>Esta tesis doctoral se enmarca dentro de la teor\u00eda de integraci\u00f3n de funciones con valores en espacios de banach. La memoria consta de una introducci\u00f3n y cinco cap\u00edtulos, el primero de ellos de car\u00e1cter auxiliar.  en el cap\u00edtulo 2 estudiamos la integral de birkhoff de funciones definidas en un espacio de probabilidad con valores en un espacio de banach. caracterizamos completamente la integrabilidad birkhoff de una funci\u00f3n vectorial en t\u00e9rminos de la familia de funciones reales formada por las composiciones de la funci\u00f3n con los elementos de la bola dual del espacio. En este sentido, la noci\u00f3n que aparece asociada a la integrabilidad birkhoff es la llamada propiedad de bourgain de una familia de funciones reales. Como aplicaci\u00f3n, reemplazamos integrabilidad pettis por integrabilidad birkhoff en la caracterizaci\u00f3n bien conocida de los espacios de banach sin copias de l1 como aquellos espacios cuyo dual tiene la propiedad d\u00e9bil de radon-nikodym. En particular, esto nos permite resolver, en el caso de espacios duales, un problema propuesto por fremlin relativo a la representaci\u00f3n de medidas vectoriales como integrales indefinidas de funciones integrables mcshane.  en el cap\u00edtulo 3 consideramos distintas teor\u00edas de integraci\u00f3n de funciones vectoriales respecto de medidas vectoriales, entre ellas la s*-integral de dobrakov (que resulta ser la extensi\u00f3n de la integral de birkhoff a este contexto) y la generalizaci\u00f3n natural de la integral de mcshane. nuestro principal teorema asegura que toda funci\u00f3n s*-integrable es integrable mcshane; el rec\u00edproco es v\u00e1lido para funciones fuertemente medibles. Probamos que tanto las funciones s*-integrables como las integrables mcshane se pueden aproximar arbitrariamente por funciones simples en la norma dada por la semivariaci\u00f3n de la integral indefinida.  en el cap\u00edtulo 4 estudiamos y comparamos varios m\u00e9todos de integraci\u00f3n (debreu, birkhoff y pettis) de multi-funciones definida<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Integraci\u00f3n en espacios de banach<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Integraci\u00f3n en espacios de banach <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jose Rodriguez Ruiz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/03\/2006<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Bernardo Cascales Salinas<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: stanimir Troyanski <\/li>\n<li> Mendoza casas Jos\u00e9 Javier (vocal)<\/li>\n<li>petr Holicky (vocal)<\/li>\n<li>robert Deville (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jose Rodriguez Ruiz Esta tesis doctoral se enmarca dentro de la teor\u00eda de integraci\u00f3n de funciones con [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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