The Monotone Convergence Theorem is a fundamental result in real analysis that deals with sequences of functions. It states that if a sequence of non-negative measurable functions is monotonically increasing and converges pointwise to a limit function, then the integral of the limit function is equal to the limit of the integrals of the functions in the sequence. This theorem is particularly useful in probability theory and statistics, as it allows for the interchange of limits and integrals under certain conditions. It ensures that if the sequence of functions approaches a limit, the area under the curve can be evaluated by taking the limit of the areas under the individual functions.