Does $P(A \cap B) = 0$ imply that $A \cap B = \emptyset$? Given that $P(A \cap B) = 0$, where  $A$ and $B$ are two events, does this   imply that $A \cap B = \emptyset$ ?
Is it not possible to have a probability zero for an event which is not empty? 
Regards. 

For continuous case, let $f(x)$ denote the probability density function for random variable $x$ (e.g. height, weight, etc). Then probability of $x$ lying between $a$ and $b$ is defined as
$P(a\le x\le b)=\int_a^b f(x)dx$.
Now what happens if you find $P(x=a)$?
