Let $(X, \Sigma, \mu)$ a measurable space and $f$ an integrable function. Show that if $(F_n)_{n\in\mathbb N}$ is a decreasing sequence of measurable sets and $F=\bigcap_{n} F_n$, then
$$\int_{F}fd\mu = \lim_{n \to \infty} \int_{F_n}fd\mu$$
Let $(X, \Sigma, \mu)$ a measurable space and $f$ an integrable function. Show that if $(F_n)_{n\in\mathbb N}$ is a decreasing sequence of measurable sets and $F=\bigcap_{n} F_n$, then
$$\int_{F}fd\mu = \lim_{n \to \infty} \int_{F_n}fd\mu$$