What's the name of the quantity $\mathbb{P}(A\cap B)/(\mathbb{P}(A)\mathbb{P}(B))\;$? In a physics book, I've come across the quantity
$$
\frac{\def\P{\mathbb{P}}\P(A\cap B)}{\P(A)\P(B)}\,,
$$
where $A$ and $B$ are events.
The author calls this quantity the correlation of $A$ and $B$, but the expression above does not agree with the definition of "correlation" that I'm familiar with.  (For one thing, when $A$ and $B$ are independent, the quantity above equals $1$, yet the correlation I'm familiar with is $0 \neq 1$ when the events are independent.) 
I must conclude that the author's word choice reflects the usage within physics.
Does this quantity have a standard name in mathematics?
 A: I think the book is simply saying that it is a measure of how correlated the two variables are. If they are totally independent (un-correlated) then $P(A\cap B)=P(A)P(B)$ and the quantity is $1$. If they are mutually exclusive the quantity is $0$. In general, $$\frac{P(A\cap B)}{P(A)P(B)}=\frac{P(A|B)}{P(A)}=\frac{P(B|A)}{P(B)}$$ So it measures what proportion of $A$ occurs "in" $B$ or vice versa.
But to answer the question, I think it's fair to say that 1) it almost certainly has some name and 2) that name is almost certainly not standard. So no - it has no name.
A: There are a number of dependence measures which are defined in similar way. For example, given two $\sigma$-fields $F$ and $G$:
$\alpha(F,G)=sup_{(A\in F,B\in G)}|P(A\cap B)-P(A)P(B)|$
$\phi(F,G)=sup_{(A\in F,B\in G)}|P(A|B)-P(A)|$
Your dependence measure defined using similar logic: 
$\delta(A,B)=\frac{P(A\cap B)}{P(A)P(B)}=\frac{P(A|B)}{P(A)}$


*

*If events $A$ and $B$ are independent $\delta(A,B)=1$

*If events $A$ and $B$ are dependent than $P(A|B)>(<)P(A)$ and $\delta(A,B)>(<)1$
A: I think "pointwise mutual information" is what comes close. PMI is defined as
$\log{\frac{p(x,y)}{p(x)p(y)}}$
