This is an announcement for the paper "Strictly positive support points of convex sets in $\mathbb{L}^0_+$" by Constantinos Kardaras. Abstract: We introduce the concept of strictly positive support points of convex sets in $\mathbb{L}^0_+$, the nonnegative orthant of the topological vector space $\mathbb{L}^0$ of all random variables built over a probability space. Traditional functional-analytic definitions fail, due to the fact that the topological dual of $\mathbb{L}^0$ is trivial when the underlying probability space is nonatomic. A necessary and sufficient condition for an element of a convex set in $\mathbb{L}^0_+$ to be a strictly positive support point of the set is given, inspired from ideas in financial mathematics. Archive classification: math.FA math.PR Remarks: 8 pages Submitted from: langostas@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.5419 or http://arXiv.org/abs/1003.5419