Volume no :10, Issue no: 2, November (2013)

Journal of Pure and Applied Mathematics: Advances and Applications

AN ELEMENTARY PROOF OF AN INFINITE DIMENSIONAL FATOU'S LEMMA WITH AN APPLICATION TO MARKET EQUILIBRIUM ANALYSIS

Author's: TAKASHI SUZUKI
Pages: [159] - [182]
Received Date: July 4, 2013
Submitted by:

Abstract

A Fatou’s lemma for the Gel’fand integrable correspondences (multifunctions) will be proved. The result will be applied to analysis of a large exchange economy on the commodity space We define the economy as a measurable map from a measure space to the space of consumers’ characteristics following Aumann [2, 4], and prove the existence of competitive equilibria.

Keywords

infinite dimensional Fatou’s lemma, large exchange economy, competitive equilibrium.