1. M(T ?i )). In contrast to Theorem B.1 above, which generalizes Theorem 2.1, i.e., the result of McAfee and Reny (1992), strictly speaking, Theorem B.3 is not simply a generalization of Theorem 3.1. Besides enlarging the range of the belief functions under consideration, from M ? (T ?i ) to M(T ?i ), we are also endowing this range with a different topology;Theorem 3.1, M ? (T ?i ) was endowed with the topology of uniform convergence of density functions, but now we endow the larger space M(T ?i ) with the topology of weak convergence of probability measures. The induced subspace topology on M ? (T ?i ) is weaker than the topology of uniform convergence of density functions
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