Lebesgue Dominated Convergence Theorem

The Lebesgue Dominated Convergence Theorem is a fundamental result in mathematics, particularly in analysis, that deals with limits of functions. It states that if you have a sequence of functions that converge to a limit, and all these functions are "dominated" by a single integrable function, then you can safely interchange the limit and the integral. This means that instead of finding the limit of a series of integrals, you can first find the limit of the functions and then integrate. This theorem is crucial for ensuring that certain mathematical operations yield consistent results in more complex settings.