Note to self: use infinitely many observable variables Xi instead of just two, and the condition for U∗ should probably be that no infinite subset of the X’s are mutually dependent (or something along those lines). Intuitively: for any “piece of latent information”, either we have infinite data on that piece and can precisely estimate it, or it only significantly impacts finitely many variables.

Note to self: use infinitely many observable variables Xi instead of just two, and the condition for U∗ should probably be that no infinite subset of the X’s are mutually dependent (or something along those lines). Intuitively: for any “piece of latent information”, either we have infinite data on that piece and can precisely estimate it, or it only significantly impacts finitely many variables.