Lebesgue integral

The Lebesgue integral is a method of calculating the total "size" or value of a function, particularly useful for handling complex functions that conventional methods might struggle with. Unlike the traditional Riemann integral, which sums up areas under curves by dividing them into small rectangles, the Lebesgue integral focuses on measuring how much the function takes on different values. This approach is particularly effective for functions defined over irregular domains or those that may not be well-behaved, making it an essential tool in advanced mathematics, especially in probability and analysis.