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An extensive literature in economics uses a continuum of random variables to model individual random shocks imposed on a large population. Let H denote the Hilbert space of square-integrable random variables. A key concern is to characterize the family of all H-valued functions that satisfy the law of large numbers when a large sample of agents is drawn at random. We use the iterative extension of an infinite product measure introduced in [6] to formulate a “sharp” law of large numbers. We prove that an H-valued function satisfies this law if and only if it is both Pettis-integrable and norm integrably bounded

Topics:
HB, QA

Publisher: University of Warwick, Department of Economics

Year: 2007

OAI identifier:
oai:wrap.warwick.ac.uk:1407

Provided by:
Warwick Research Archives Portal Repository

Downloaded from
http://wrap.warwick.ac.uk/1407/1/WRAP_Hammond_twerp_806.pdf

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