Lebesgue integration

Lebesgue integration is a mathematical method for measuring the total size or value of a function over a region, especially when the function may be complex or irregular. Unlike the traditional Riemann approach, which sums values over small intervals, Lebesgue integration partitions the range of the function into levels and measures how much of the input space corresponds to each level. This allows for more flexible and powerful integration, particularly useful in advanced analysis and probability, where functions may be discontinuous or not well-behaved. Ultimately, Lebesgue integration extends the concept of summing to a broader class of functions.