Before revision:  The D C rule also offers one interpretation of the Fair Share when utilities are neither additivenor monotonic . Under a mild continuity assumption, it guarantees to each agent her minMax utility : that of her best share in the worst possible partition.
After revision:  The D n of the utility of a heterogenous non atomic cake, if utilities are additive. The minMax utility of an agent is that of her best share in the worst possible partition.