We consider the space of all set functions defined on a finite set S. This space is a linear space whose dimension is 2( S ). The set of all polymatroid functions is a convex cone in that space. We investigate conditions for a polymatroid function to be extremal in the cone. To handle the extremal problem of set functions easily, we treat the Mobius inverse forms of set functions. Moreover, we give the notions of compressedness and uniformity, which are satisfied by matroid functions. We discuss the extremality on compressed and uniform submodular functions. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 10]
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机译：我们考虑在有限集S上定义的所有集合函数的空间。该空间是线性空间，其维数为2（ S ）。所有多拟仿函数的集合是该空间中的凸锥。我们调查了一个条件，在锥体锥端的多类脉动功能。为了轻松处理集合函数的极端问题，我们对待集合函数的Mobius逆形式。此外，我们给出了拟阵函数满足的压缩性和均匀性的概念。我们讨论压缩和统一子模函数的极值。 （C）2000 Elsevier Science B.V.保留所有权利。 [参考：10]
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