What's the measure of $A=\cap_{i=1}^\infty A_i$ for a monotone class when $A_i=\infty$ for all $i$

Question

As the title said, I know the examples in which $m(A)=0$ or $m(A)=\infty$. But I want to know if $m(A)$ can be equal to any other values.

Answer 1

Pick your favourite example with $m(A)=0$, a set $U$ with $m(U)=\alpha$, and consider $B_i=A_i\cup U$.