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# The index satisfies mean independence, or income homogeneity, axiom: if all incomes are multiplied by a positive constant, the inequality remains the same: <math>A_\varepsilon(y_1,\ldots,y_N) = A_\varepsilon( ky_1,\ldots,ky_N)</math> for any <math>k>0</math>.
# The index is subgroup decomposable.<ref>Shorrocks, AF (1980). The class of additively decomposable inequality indices. ''Econometrica'', 48 (3), 613–625, {{doi|10.2307/1913126}}</ref> This means that overall inequality in the population can be computed as the sum of the corresponding Atkinson indices within each group, and the Atkinson index of the group mean incomes:
::: <math>
A_\varepsilon(y_{gi}: g=1,\ldots,G, i=1,\ldots,N_g) = \sum_{g=1}^G w_g A_\varepsilon( y_{g1}, \ldots, y_{g,N_g}) + A_\varepsilon(\mu_1, \ldots, \mu_G)
</math>
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