Sure Wins, Separating Probabilities and the Representation of Linear Functionals

Details Sure Wins, Separating Probabilities and the Representation of Linear Functionals Sure Wins, Separating Probabilities and the Representation of Linear Functionals

2007-09-21

arxiv.org/abs/0709.3411v2

Mathematics

Functional Analysis

Scientific paper

We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

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