关于$L^\infty$的Kreps-Yan定理
The Kreps-Yan theorem for $L^\infty$
摘要：
我们证明了Kreps-Yan定理的以下版本。对任意范数闭凸锥$C\subset L^\infty$，使得$C\cap L_+^\infty=\{0\}$和$C\supset -L_+^\infty$，存在一个严格正连续线性泛函，它对$C$的限制是非正的.证明使用了一些工具，从凸分析在对比的情况下，弱Lindelöf巴拿赫空间，这种方法是不需要的。
英文摘要：
We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone $C\subset L^\infty$ such that $C\cap L_+^\infty=\{0\}$ and $C\supset -L_+^\infty$, there exists a strictly positive continuous linear functional, whose restriction on $C$ is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindelöf Banach space, where such approach is not needed.
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