Sure Wins, Separating Probabilities and the Representation of Linear Functionals
Abstract
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
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.3411
 Bibcode:
 2007arXiv0709.3411C
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Probability;
 28A25;
 28C05
 EPrint:
 Journal of Mathematical Analysis and Applications 2009