Fatou's Lemma is a fundamental result in measure theory, which deals with the behavior of sequences of measurable functions. It states that for a sequence of non-negative measurable functions, the limit of the integral of the limit inferior of these functions is less than or equal to the limit inferior of the integrals of the functions. In simpler terms, it provides a way to interchange limits and integrals under certain conditions. This lemma is particularly useful in probability theory and analysis, as it helps in establishing convergence properties of integrals. It ensures that even if the functions do not converge pointwise, we can still make meaningful statements about their integrals.