Unformatted text preview: Let X be a set. We denote by | X | the number of members of X . A partition of X is a collection of disjoint subsets of X whose union is X . Let N be a finite set and let be a set. Then is Pareto efficient if there is no for which y i > x i for all is strongly Pareto efficient if there is no for which for all and y i > x i for some . A probability measure μ on a finite (or countable) set X is an additive function that associates a nonnegative real number with every subset of X (that is, whenever B and C are disjoint) and satisfies μ ( X ) = 1. In some cases we work with probability measures over spaces that are not necessarily finite. If you are unfamiliar with such measures, little is lost by restricting attention to the finite case; for a definition of more general measures see, for example, Chung (1974, Ch. 2)....
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- Spring '10
- Set Theory, Chung, nonnegative real numbers, xi > yi