Before revision:  They are also inconsistent under aggregation and mixing distributions, as weighted concentration measures for A and B will tend to be lower than that from A + B. In addition, it can be shown that under  fat tails, increases in the total sum need to be accompanied by increased measurement of concentration .
After revision:  They are also inconsistent under aggregation and mixing distributions, as weighted concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under fat tails, increases in the total sum need to be accompanied by increased measurement of concentration .