Lebesgue Dominating Convergence Theorem
In calculus we learn about the Riemann integral of a function, which certainly works for many functions. Unfortunately, we must use the word ‘many’. Lebesgue measure, and from this the Lebesgue integral, will allow us to define the right notion of integration. Not only will we be able to integrate far more functions with the Lebesgue integral but we will also understand when the integral of a limit of ...