Dominated convergence theorem

The Dominated Convergence Theorem is a principle in mathematics that helps us understand how functions behave under limits. It states that if you have a sequence of functions that converge to a certain function and are all "bounded" by another function (which doesn’t grow too large), then you can interchange the process of taking limits and integrating. In simpler terms, if you can show that one function limits another in a consistent way, you can evaluate their areas under curves step-by-step, ensuring that the limits hold true throughout the process. This is useful in various fields, including probability and analysis.