Measure Theory and Integration

This book offers a rigorous, comprehensive, and modern presentation of the most traditional concepts in measure theory and integration.Building on the classical foundations, it introduces the theory with full generality and meticulous attention to detail, following the stylistic tradition first introduced by Nicolas Bourbaki.The book is designed for graduate students and young researchers seeking a thorough exposition of the theory in an abstract setting, complete proofs, and the strategies underlying them, fostering good mathematical habits in logical reasoning and clarity of deduction. Beyond standard treatments, the book features several distinctive elements: Some classical results, such as Radon-Nikodým theorem, and Lebesgue and Hahn decompositions, have been presented with original proofs, aimed to clarifying the logic behind the results; some topics that are often overlooked, such as kernels, uniform integrability, the Vitali-Hahn-Saks and Dunford-Pettis theorems are developed in