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The Monotone Convergence Theorem is applicable even when the integrals of the functions $(f_n)$ are infinite. It ensures that the limit of the sequence of functions, when integrated, will either converge to the same infinite value or a finite value.

In the context of the Monotone Convergence Theorem, the functions $(f_n)$ in the sequence must be non-negative. This means that for almost every point in the domain, $f_n(x) \geq 0$ for all $n$.

The Monotone Convergence Theorem states that if a sequence of functions $(f_n)$ satisfies the given conditions, it converges to a limit function $f$ almost everywhere.

The functions in the sequence must be measurable with respect to the given sigma-algebra. A measurable function is one whose pre-images of Borel sets are in the sigma-algebra.

A conclusion of the Monotone Convergence Theorem is that the integral of the limit function $f$ is equal to the limit of the integrals of the functions in the sequence, i.e., $\lim_{n \to \infty} \int f_n = \int \lim_{n \to \infty} f_n = \int f$.