Lebesgue Integration is a mathematical concept that extends the idea of integration beyond traditional methods, such as Riemann Integration. It focuses on measuring the size of sets and functions, allowing for the integration of more complex functions, especially those that may be discontinuous or not well-behaved. In Lebesgue Integration, functions are integrated by measuring the values they take and the sets of points where they take those values. This approach provides a more flexible framework for analysis, making it easier to work with limits and convergence, which is essential in various fields of mathematics and applied sciences.