Space as a union of disjoint union and intersection

Question

Let $(X,\mu)$ and $E_n\subset X$ s.t $\mu(E_n)=\mu(X)$

can we write $$\mu(X)=\mu(\cap_{n=1}^{\infty}E_n\uplus (\cap_{n=1}^{\infty}E_n)^C)$$?

Shouldn't it be:

$$\mu(X)=\mu(\cup_{n=1}^{\infty}E_n\uplus (\cap_{n=1}^{\infty}E_n)^C)$$?

Answer 1

$X$ is the disjoint union of $\cap E_n$ and $(\cap E_n)^{c}$ so the first one is correct (without any assumptions on the sets $E_n$).