This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.