In one of my classes the lecturer referred to "the range space being (or not being) rectangular" as a justification of independence (or not) of two variables.

I don't understand what this use of 'rectangular' means specifically. Could someone give me a quick explanation. A Google search doesn't seem to turn anything up.

From the context it seems to mean that the variables have some sort of orthogonality (and that seems to be an intuitive definition of 'rectangular'), that is that they are not dependent on each other. But, in my head I feel like I'm just begging the question rather than understanding the concept on it's own.

How would you prove that a range space is rectangular? Do you just show that the value of one is not dependent on the other? But, again, it seems to me like I'm saying, 'They're independent because they're not dependent', and that's not very satisfying.

Thanks!