Introdução à teoria da medida e integração de Lebesgue

Abstract

The present course conclusion work is an introductory bibliographic review about Lebesgues’s Measure Theory and Integral and has as objective to complement the knowledge acquired at graduation. We seek to integrate functions that aren’t integrable by Riemann’s Integral, for this we started the study of preliminary concepts as Sequences, Isolated point, Accumulation point, Supreme, Lowest, Diameter, Open Set, Closed Set, enumerable, non-enumerable, limited variation function, function’s sequences, punctual convergence, limited uniform function, uniform convergent. So we precede the study of Measure, Lebesgue’s Exterior Measure, Mensurable sets, Lebesgues’s Measure, Mensurable Functions, Egorov and Lusin’s Theorem, Measure Convergence, Lebesgue’s Integral and lastly the Convergence Theorems