Extend exercise 3.210 to allow for noncompact Si, thus proving the Shapley-Folkman theorem. Exercise 3.210 Let {S1,

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Extend exercise 3.210 to allow for noncompact Si, thus proving the Shapley-Folkman theorem.
Exercise 3.210
Let {S1, S2, . . . , Sn} be a collection of nonempty compact subsets of an m-dimensional linear space, and let x ˆˆ conv

We consider the Cartesian product of the convex hulls of Si, namely

Every point in P is an n-tuple (x1, x2, . . . , xn) where each xi belongs to the corresponding conv Si. Let P(x) denote the subset of P for which

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Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

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Question Posted: May 02, 2016 11:44 AM

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Extend exercise 3.210 to allow for noncompact Si, thus proving the Shapley-Folkman theorem. Exercise 3.210 Let {S1,

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P - IIconv S, Σ2l Xi = X, that is, P(x) = (Xi, X2, . . . , Xn ) : Xi E conv S, and Σ x,-x

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Let 1 2 be a collection of nonempty subsets of an dimensional linear space and let x conv That ...View the full answer

Foundations of Mathematical Economics

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