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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 659814, 9 pages
http://dx.doi.org/10.1155/2014/659814
Research Article

The Burkill-Cesari Integral on Spaces of Absolutely Continuous Games

1Dipartimento di Studi per l'Economia e l'Impresa, Università del Piemonte Orientale, Via Perrone 18, 28100 Novara, Italy
2Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy

Received 31 July 2013; Accepted 18 January 2014; Published 10 March 2014

Academic Editor: Jewgeni Dshalalow

Copyright © 2014 F. Centrone and A. Martellotti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that the Burkill-Cesari integral is a value on a subspace of and then discuss its continuity with respect to both the and the Lipschitz norm. We provide an example of value on a subspace of strictly containing as well as an existence result of a Lipschitz continuous value, different from Aumann and Shapley’s one, on a subspace of .