Three (marginal?) questions regarding convergence

This paper focuses on three (marginal?) questions surrounding the analysis of economic convergence and uses Spanish provinces as a means of illustration. The three questions in hand are as follows. Given that the geographical units of analysis are usually quite different in economic size, is the weighting of economic units relevant in convergence analysis? The average per capita income of a given region, or country, is the first moment in the distribution of income, but what about the second moment, inequality, have we converged in inequality? An aggregate welfare index must take into account, at least, the evolution of the first two moments of the distribution of income, and so does the adjustment for inequality make important differences in the evolution of average per capita income? The answer to the first two questions is yes, but to the third it is clearly no.