The Lebesgue Dominated Convergence Theorem is a fundamental result in real analysis that provides conditions under which the limit of a sequence of functions can be interchanged with the integral. Specifically, if a sequence of measurable functions converges pointwise to a function and is dominated by an integrable function, then the integral of the limit equals the limit of the integrals. This theorem is particularly useful in probability theory and functional analysis, as it allows for the simplification of complex integrals. It ensures that under certain conditions, we can safely pass limits inside integrals, preserving the integrity of the calculations.