Gerard Debreu on the Integration of Correspondences ∗
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چکیده
In 1967, Gerard Debreu presented an integral of a correspondence by taking a higherdimensional point of view whereby a correspondence is seen as a function in a Banach space and thereby integrated as a consequence of the theory of Bochner integration. In this survey paper, we locate Debreu’s paper from the viewpoint of subsequent work, both in the theory of embeddings of convex-valued correspondences as functions in a Banach space and the application of Bochner and Gelf’and integration in mathematical economics. We also follow up Debreu’s suggested parallelism between two lines of development, the “statistical one and the economic one,” by presenting the authors’ recent results on integration of correspondences with respect to a vector measure. Working draft of a paper being prepared for possible presentation at the 2005 NBER/NSF/CEME Mathematical Economics Conference to be held at Berkeley together with a memorial in honor of Gerard Debreu. Journal of Economic Literature Classification Numbers: C07, DO5.
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تاریخ انتشار 2005