Existence of nonatomic core-walras allocations

We prove the existence of Walras allocations, where allocations are understood as measures on a nonatomic Boolean algebra. The algebra need not be a σ-algebra, as usually assumed, and the measures need not be countably additive and need not have densities with respect to the endowment allocation. Except for a strengthening of the continuity hypothesis, this is the framework we used earlier to prove the equivalence of core and Walras allocations. Our proof rests on two propositions of special interest in their own right: one asserts extensibility of coalition preferences, and the other characterizes coalition preferences.