Measure and Integration

AbstractThis textbook provides a rigorous and pedagogically structured introduction to measure and integration theory for third-year undergraduate students in mathematics. Beginning with the essential foundations of set theory, countability, and measurable spaces, it progressively develops the theory of measures, the construction of the Lebesgue measure and integral, and the fundamental convergence theorems. The text continues with the study of L^p spaces, including their principal inequalities and completeness properties, and concludes with product measures, the Fubini-Tonelli theorem, and comprehensive synthesis problems. Emphasis is placed on mathematical rigor, intuitive understanding, and problem-solving through detailed proofs, illustrative figures, and a large collection of fully solved exercises. Designed in accordance with the LMD curriculum, this book serves both as a course text and as a self-study reference, preparing students for advanced studies in functional analysis, probability theory, and partial differential equations.