The Riesz Representation Theorem for Lp.

• Grant number: 24/23317-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Janaina Pedroso Zanchetta
• Grantee: Daniel Augusto Poltronieri Neves
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

This scientific initiation project aims to introduce the student to Measure and Integration Theory, focusing on the understanding and study of fundamental concepts such as sigma-algebras, measurable sets and functions, measures, Lebesgue integration and Lebesgue spaces, as well as important properties and results related to this theory. The study will culminate in the understanding and demonstration of the Riesz Representation Theorem in Lp. The study of these notions will allow the scholarship holder to come into contact with important Analysis techniques.