Teoria da medida e critério de Lebesgue para Riemann integrabilidade

Abstract

The thesis addressed important concepts in measure theory and their application in the theory of integration. Topics such as measure, Lebesgue measure, Lebesgue integration theory, set of measure zero, discontinuity, Lebesgue criterion for Riemann integrability, and the monotone convergence theorem were explored. The research emphasized the relevance of these concepts for understanding the integration of functions and the relationship between Lebesgue and Riemann methods. In particular, the Lebesgue criterion for Riemann integrability was investigated as a necessary and sufficient condition for the existence of the Riemann integral in certain functions. The study contributed to deepening theoretical knowledge in this field and expanded the understanding of different approaches to integration in mathematical analysis.