This is an announcement for the paper "Sure wins, separating probabilities and the representation of linear functionals" by Gianluca Cassese. 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 Archive classification: math.FA math.PR Mathematics Subject Classification: 28A25, 28C05 The source file(s), JMAAR1.tex: 32542 bytes, is(are) stored in gzipped form as 0709.3411.gz with size 11kb. The corresponding postcript file has gzipped size 283kb. Submitted from: g.cassese@economia.unile.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0709.3411 or http://arXiv.org/abs/0709.3411 or by email in unzipped form by transmitting an empty message with subject line uget 0709.3411 or in gzipped form by using subject line get 0709.3411 to: math@arXiv.org.