This is an announcement for the paper "Almost limited sets in Banach lattices" by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji. Abstract: We introduce and study the class of almost limited sets in Banach lattices, that is, sets on which every disjoint weak$^{*}$ null sequence of functionals converges uniformly to zero. It is established that a Banach lattice has order continuous norm if and only if almost limited sets and $L$-weakly compact sets coincide. In particular, in terms of almost Dunford-Pettis operators into $c_{0}$, we give an operator characterization of those $\sigma$-Dedekind complete Banach lattices whose relatively weakly compact sets are almost limited, that is, for a $\sigma$-Dedekind Banach lattice $E$, every relatively weakly compact set in $E$ is almost limited if and only if every continuous linear operator $T:E\rightarrow c_{0}$ is an almost Dunford-Pettis operator. Archive classification: math.FA Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65 Remarks: 11 pages Submitted from: jinxichen@home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.2020 or http://arXiv.org/abs/1309.2020