APPLICATION OF THE LEBEGUE INTEGRAL AND MEASURE THEORY IN MATHEMATICAL MODELING

This article provides an overview of the fundamentals of the Lebesgue integral and measure theory, and their applications in mathematical modeling, probability theory, and various mathematical problems. It discusses the differences between the traditional Riemann integral and the Lebesgue integral, the concept of Lebesgue measure, and the role of sigma-algebras. Practical examples illustrate the advantages and unique characteristics of these methods.