We use constructive measure theory to show the decidability pf the "almost all" theory of subrecursive degrees. The formulas of this theory are built up using the constant 0 standing for the minimum degree, the functions $\cup,\cap$ standing for the join and meet of two degrees respectively, the relation $\leq$ standing for the reducibility-ordering, the logical connectives "ampersand", $\neg$ and the quantifier (almost $\forall$ a). An efficient decision procedure is described.