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 a introductory study of the main results on 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 by a review of some results on metric and Banach spaces. The Hanh-Banach theorem will be of our interest and also the Lp spaces.