Let $(\Omega,\mathcal{A},\mu)$ be a measure space, and let $A,B\in\mathcal{A}$ be two sets. In the proof I'm working on, the number $\mid \mu(A\cap B)-\mu(A)\mu(B)\mid $ will appear many times. I would like to simplify the notation to something like: "define the function $f(A,B)=\mid \mu(A\cap B)-\mu(A)\mu(B)\mid$ for $\mathcal{A}$-measurable sets $A,B$". In this case, I would just use $f(A,B)$ which is much simpler than the former.
Is there something wrong with this map? Can I use it to substitute $\mid \mu(A\cap B)-\mu(A)\mu(B)\mid $?
This function seems to be defined on the measurable space $(\Omega\times\Omega,\mathcal{A}\otimes\mathcal{A})$, and I'm not secure if there are issues involved.
Thanks in advance