Measure Theory and Integration

This group gathers theorems from measure theory, the framework built by Lebesgue and others for assigning a size to sets and integrating functions far more general than the ones ordinary calculus can handle. It covers the convergence theorems, including the dominated and monotone convergence theorems and Fatou's lemma, that justify exchanging a limit with an integral, together with Fubini's theorem for integrating over several variables at once, the Radon-Nikodym theorem relating one measure to another, and further results on how measurable functions and sets can be approximated or covered.