Products of capacities on separate spaces through additive measures

An approach to product of capacities is proposed. It extends our previous approach which works only for a special class of capacities. The main advantage of our approach, as opposed to most approaches given so far, is that it is designed for general, i.e. not necessarily discrete, monotone capacities. The product is not defined uniquely but rather, a lower and upper bound are given, which in case where both capacities are additive measures both coincide with the usual additive product.