# Math Help - signed measure

1. ## signed measure

For nonnegative $f,g \in L^1(X,F,\mu)$ and sub $\sigma$algebra $\Lambda$ which is not a subset of $F$, define $v(A)=\int_A (f-g) d\mu$ for all $A \in \Lambda$.
Show that $v$ is a signed measure.

i got confused here. since $\Lambda$ is not a subset of $F$, how do i find the integral? can i integrate it only when $A$ is an element of $F$?

2. Originally Posted by GTO
For nonnegative $f,g \in L^1(X,F,\mu)$ and sub $\sigma$algebra $\Lambda$ which is not a subset of $F$, define $v(A)=\int_A (f-g) d\mu$ for all $A \in \Lambda$.
Show that $v$ is a signed measure.

i got confused here. since $\Lambda$ is not a subset of $F$, how do i find the integral? can i integrate it only when $A$ is an element of $F$?
If $A$ is not in $F$, then what is $v(A)=\int_A (f-g) d\mu$? is it zero or undefined?