An introduction to the Lebesgue integral

• Grant number: 11/22385-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2012
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Juliana Conceição Precioso Pereira
• Grantee: Marcelo Adriano dos Santos Bongarti
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

In the first moment, the aim of the measure theory and integration is to provide the basis for the intuitive notions of length, area, volume, etc. ... Such quantities are generically referred to as measures and it is up to the measure theory not only to give accurate definitions of such concepts but also determine which classes of sets are measurable. However, this theory is not restricted to dealing with geometric concepts such as length, area, etc ..., the study of the concept of measure and measurable sets, but has as its most important role the formalization of the theory of integration. The old notion of area view as the "area under the graph "of a function allows us to conclude that the concepts of measure and integral are connected. In this paper, we study the Lebesgue integral that broadens, in a remarkable way, the class of the Riemann integrable functions.(AU)