Measure and Integration

The course "Measure and Integration" is divided into two main parts to offer a comprehensive understanding of measure theory and its applications. The first part emphasizes measure theory, acquainting students with the fundamental notions of measures, measurable sets, and measurable functions. Essential subjects encompass sigma-algebras, measure characteristics, and the formulation of many measure types, establishing a foundation for rigorous mathematical analysis. The second part highlights the Lebesgue measure, exploring its significance in the context of integration. Students will study Lebesgue integration, convergence theorems, and the relationship between Lebesgue and Riemann integrals. Through a combination of theoretical insights and practical applications, this course equips students with the tools to tackle advanced problems in analysis, probability, and related fields.