%0 Journal Article %T Linear $¦Ò$-additivity and some applications %A Tal Orenshtein %A Boaz Tsaban %J Mathematics %D 2009 %I arXiv %X We show that countable increasing unions preserve a large family of well-studied covering properties, which are not necessarily sigma-additive. Using this, together with infinite-combinatorial methods and simple forcing theoretic methods, we explain several phenomena, settle problems of Just, Miller, Scheepers and Szeptycki [COC2], Gruenhage and Szeptycki [FUfin], Tsaban and Zdomskyy [SFT], and Tsaban [o-bdd, OPiT], and construct topological groups with very strong combinatorial properties. %U http://arxiv.org/abs/0906.5136v3