 Definition.Let formula_21 be a metric space with its Borel formula_22-algebra formula_23.A bounded sequence of positive probability measures formula_24 on formula_25 is said to converge weakly to the finite positive measure formula_26 (denoted formula_27) if any of the following equivalent conditions is true (here formula_28 denotes expectation or the formula_29 norm with respect to formula_30, while formula_31 denotes expectation or the formula_29 norm with respect to formula_26)