This paper is concerned with the Aumann integral for integrands of the form F(a) = [G(a) − e(a)] [ {0}, where is a simple multifunction with values in the hyperspace of closed and convex values of a Banach space X. Integrands of this form are those that occur in the core-Walras equivalence, where a represents the single agent of an atomless economy, e is the initial endowement. However in our model the underlying measure (measuring the power of infleuence of coalitions) is assumed to be simply finitely additive. More precisely e give some results about the convexity of a pair of finitely additive measures and we apply them to derive the convexity of the Aumann integral when X is a Banach latice and the initial endowement satisfies suitable assumptions
A note on Lyapounov-like theorem for some finitely additive measures and applications
MARTELLOTTI, Anna;SAMBUCINI, Anna Rita
2005
Abstract
This paper is concerned with the Aumann integral for integrands of the form F(a) = [G(a) − e(a)] [ {0}, where is a simple multifunction with values in the hyperspace of closed and convex values of a Banach space X. Integrands of this form are those that occur in the core-Walras equivalence, where a represents the single agent of an atomless economy, e is the initial endowement. However in our model the underlying measure (measuring the power of infleuence of coalitions) is assumed to be simply finitely additive. More precisely e give some results about the convexity of a pair of finitely additive measures and we apply them to derive the convexity of the Aumann integral when X is a Banach latice and the initial endowement satisfies suitable assumptionsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
