This is an announcement for the paper "Characterization of compact subsets of $\mathcal{A}^p$ with respect to weak topology" by Hirbod Assa. Abstract: In this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak topology induced by $\mathcal{A}^p$, was recently employed to create the convex risk theory of random processes. The weak compact sets of $\mathcal{A}^p$ are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on $\mathcal{R}^q$ and for their use in the optimization theory. Archive classification: math.PR math.FA Remarks: 8 pages The source file(s), compactsetsAssa.H.tex: 19008 bytes, is(are) stored in gzipped form as 0804.2873.gz with size 6kb. The corresponding postcript file has gzipped size 67kb. Submitted from: assa@dms.umontreal.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2873 or http://arXiv.org/abs/0804.2873 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2873 or in gzipped form by using subject line get 0804.2873 to: math@arXiv.org.