I'm currently working on a homework question, and I am stuck. I copied this off the whiteboard, so it is very possible that I made a mistake in transcribing it. Of course I may be misinterpreting something, and if that is the case, I would like some clarification.
We are given that $(X,M,\mu)$ is a measure space. For $A,B\subset X$, we have that $A\triangle B = (A\setminus B)\cup (B\setminus A)$. We then have that $d(C_1,C_2) = \mu(A\triangle B)$ for $A\subset C_1$ and $B\subset C_2$. We are supposed to prove that $d$ is a well-defined distance function, but I don't see how that is possible. I feel like I could complete the proof if $d(A,B)=\mu(A\triangle B)$, but that is not what I am given. Any hints would be appreciated.
Edit: Yes, $C_1, C_2\in M$.
Edit: Haha, the last guess was right. It's 4:00AM where I'm living currently, but I found someone who was awake and he gave me the correct answer. Thanks for your help everyone.