Random variable X (as a measureable function from some probability space to the reals) has support S and image T. True or False:
i.) S is always a subset of T.
ii.) (S,E,dF) is the induced probability space with: sample space S, events E the intersections of S with the Borel sets, and dF the probability measure derived from F -the distribution of X.
(As S is the smallest closed subset of reals R with probability 1, it is a subset of the closure of T. The two issues come from having read somewhere that the support is, "loosely" speaking, the outcomes X can take on mapping the space to R. Started with case T finite.)