| THE STRICT POSITIVITY IN A NONSTANDARD HULL AND ITS APPLICATIONS TO ECONOMICS |
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| 作者姓名： | WU Kangping |
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| 作者单位： | Institute of Quantitative Economics，North China University of Technology，Beijing 100041，China |
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| 摘 要： | 1.IntroductionThenonstandardhull,originallyintroducedbyLuxemburgin1],hasprovedtobeausefultoolinstudyingthelocaltheoryofBanachspacesandnormedRieszspaces.Asystematictheoryinthisaspectisdevelopedin2--4].However,peoplepaylessattentiontostrictlypositivevecto…
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THE STRICT POSITIVITY IN A NONSTANDARD HULL AND ITS APPLICATIONS TO ECONOMICS |
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| WU Kangping.THE STRICT POSITIVITY IN A NONSTANDARD HULL AND ITS APPLICATIONS TO ECONOMICS[J].Journal of Systems Science and Complexity,1997(2). |
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| Authors: | WU Kangping |
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| Abstract: | The purpose of this paper is to study the strict positivity in a nonstandard hull of an internal normed Riesz space. Several characterizations are obtained for an element of the hull to be strictly positive. Particularly, it is shown that a nonstandard hull of an internal normed Riesz space has strictly positive elements if and only if it has an order unit. This result has an application to the double infillity problem in economics. It follows that the existence of equilibria in a nonstandard double infinity economy is equivalent to the existence of finite equilibria. |
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| Keywords: | Strict positivity nonstandard hull internal normed Riesz space infinity economy |
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