Introduction to measure theory and functional analysis

• Grant number: 14/03435-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2014
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Anderson dos Santos Gonzaga
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project, it is proposed an introductory study of the main results of Measure Theory and Functional Analysis. We start with some important subjects on Measure Theory by studying a regular course of Real Analysis which is part of the Graduate Program in Computational Mathematics of the FCT-Unesp. As far as Functional Analysis is concerned, we start with a review of some results on metric and Banach spaces. The Hanh-Banach theorem will be of interest as also the Lp spaces.(AU)