Properties of ideals on the generalized Cantor spaces

We define a class of productive sigma -ideals of subsets of the Cantor spac e 2(omega) and observe that both sigma -ideals of meagre sets and of null s ets are in this class. From every productive sigma -ideal J we produce a si gma -ideal J(kappa) of subsets oft he generalized Cantor space 2(kappa). In particular, starting from meagre sets and null sets in 2(omega) we obtain meagre sets and null sets in 2(kappa), respectively. Then we investigate ad ditivity, covering number, uniformity and cofinality of J(kappa). For examp le, we show that non(J) = non(J omega (1)) = non(J omega (2)). Our results generalizes those from [5].