Convex analysis for sets of local martingales measures

Josef Štěpán; P. Ševčík

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Let $Ω_{1}, ..., Ω_{n}$ be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone $C$ of the cone of positive $n$ -superharmonic functions in $Ω_{1} \times ... \times Ω_{n}$ is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of $C$ . The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary...