A lattice can be represented by a discrete subspace which spans the vector space [tex]R^n[/tex]. Any point which cannot be generated from the basis vectors by a linear combination with integer coefficients is a non-lattice point (a point with at least one irrational coordinate).

Yeah, that's the only mathematical notion of lattice I am familiar with. Like in crystal structures. But I wasn't sure what it meant in this context: "nonlattice random variables". Is it just a fancy way of saying that the random variables are continuous--or that they attain their limiting values or something like that?

A "lattice" random variable has all values integer multiples of some one number. This is not the same as "discrete" random variable. For example, if [itex]X[/itex] has only the values 1 and [itex]\sqrt{2}[/itex] is would be discrete but not lattice.

OK. So a discrete RV can be non-lattice provided it ranges over a countable set? (It's a rhetorical question. No need to respond unless you disagree.) Thanks.