Let (12. A) denote a measurable space, and let M(12) denote the set of all probability measures on A. a) Show that d(P,Q) = sup |P(A) - Q(A)], = P, Q E M(12), Ae defines a metric on M(92). b) Prove or disprove the continuity of the mapping ]0,00[ + M(R): 1 HA(), where (1) denotes the Poission distribution with parameter .. c) Assume that I is a complete separable metric space and that A is the corresponding Borel o-algebra. Characterize those spaces, where convergence w.r.t. d is equivalent to weak convergence. Let (12. A) denote a measurable space, and let M(12) denote the set of all probability measures on A. a) Show that d(P,Q) = sup |P(A) - Q(A)], = P, Q E M(12), Ae defines a metric on M(92). b) Prove or disprove the continuity of the mapping ]0,00[ + M(R): 1 HA(), where (1) denotes the Poission distribution with parameter .. c) Assume that I is a complete separable metric space and that A is the corresponding Borel o-algebra. Characterize those spaces, where convergence w.r.t. d is equivalent to weak convergence