1. Jan 12, 2009

DeanSkerl

Im an applied statistician who hasnt looked at this stuff in years (And even then never took a class in it formally). So try and forgive me if my language is sloppy.

Consider the space of all d-dimensional bounded random vectors, L_infinity. Its Banach, hence complete and closed.

Consider a single fixed d-dimensional random vector in L1. Lets call it X.

Is the set

{aX : a is in L_infinity} necessarily closed? Here Im considering the dot product so that aX is a random variable.

Any help, references, etc would be greatly appreciated.

Best regards,
--Scott