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.