Riemann integral vs Lebesgue integral
Riemann integral vs Lebesgue integral
Riemann integral : In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented to the faculty at the University of Göttingen in 1854, but not published in a journal until 1868.[1] For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration. Learn more
Lebesgue integration : In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The Lebesgue integral extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. Learn more
Here, I explain the differences between the Riemann integral and the Lebesgue integral in a demonstrative way.