Introduction to the Lebesgue spaces and to the functional analysis

• Grant number: 17/22781-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2017
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcos Tadeu de Oliveira Pimenta
• Grantee: Ramon Batista de Campos
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project we propose an introductory study of the main results in Functional Analysis and the Lebesgue Spaces. First of all the student is going to study several topics in Metric Spaces, which will be the basis to proceed to the study of the main topics in Functional Analysis and then to the Lebesgue spaces. We propose studying normed vectorial spaces, topological results that allow us to state the Baire Theorem and its consequences. To end up, we propose the study of the Lebesgue spaces. (AU)