Abstract
In this article, we study upper exhausters of positively homogenous functions defined on locally convex space. We prove the existence of minimally fine exhauster finer than the given one. Such exhauster has to be unique for two-element exhauster. We show that a positively homogenous function is upper semicontinuous if and only if it has an upper exhauster. We prove that Clarke subdifferential of a positively homogenous function is the closed convex hull of the union of its minimally fine exhauster. We also present a number of appropriate examples.
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