渐近锥几个定义的等价性和性质及其在经济学中的应用

Equivalence of several definitions and properties of asymptotic cone and its applications in economic theory

在Jean-Baptiste等(2004)、Tyrrell(1970)和Debreu(1959)给出不同的渐近锥定义的基础上,在附加凸性的条件下证明了这几个渐近锥定义的等价性,并利用这种等价性给出了渐近锥的几个重要性质的另外一种证明方法,最后讨论了渐近锥在经济学中的应用。

On the basis of different definitions of asymptotic cone provided by Jean-Baptiste, （2004）, Tyrrell （1970） and Debreu（1959） ,this paper proves the equivalence of these definitions of asymptotic cone under the additive condition of convexity, Using this equivalence, it proves several important prop-erties of asymptotic cone in another way. Finally conomic theory. , it discusses the applications of asymptotic cone in economic theory.