The Lebesgue integral is a method of integration that extends the concept of the integral to a broader class of functions and allows for the integration of functions defined on measurable sets. It is based on the idea of measuring the size of sets and sums, facilitating the handling of limits and convergence in a more flexible way compared to traditional Riemann integration. This integral is crucial for working with measurable functions and provides the foundation for various applications in probability, real analysis, and geometric measure theory.
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