Abstract
A correspondence is a set-valued function. That is, a correspondence associates to each point in one set a set of points in another set. As such, it can be viewed simply as a subset of the Cartesian product of the two sets. It may seem a bit silly to dedicate two chapters to such a topic, but correspondences arise naturally in many applications. For instance, the budget correspondence in economic theory associates the set of affordable consumption bundles to each price-income combination; the excess demand correspondence is a useful tool in studying economic equilibria; and the best-reply correspondence is the key to analyzing noncooperative games. The theory of “differential inclusions” deals with set-valued differential equations and plays an important role in control theory.
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© 1999 Springer-Verlag Berlin Heidelberg
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Aliprantis, C.D., Border, K.C. (1999). Correspondences. In: Infinite Dimensional Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03961-8_16
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DOI: https://doi.org/10.1007/978-3-662-03961-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65854-2
Online ISBN: 978-3-662-03961-8
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