Heinz’s inequality and Bernstein’s inequality

Corruption And Inequality

Education , Inequality and Income Inequality

In this paper we propose to measure inequality of educational achievements by constructing a Gini index on educational attainments. We then use the proposed measure to analyse the relationship between inequality in incomes and educational achievements (in terms of both the average attainments and its concentration). Even if theoretical considerations suggest a non-linear relationship between th...

Lévy’s inequality, Rademacher sums, and Kahane’s inequality

Let (Ω,A , P ) be a probability space. A random variable is a Borel measurable function Ω→ R. For a random variable X, we denote by X∗P the pushforward measure of P by X. X∗P is a Borel probability measure on R, called the distribution of X. A random variable X is called symmetric when the distribution of X is equal to the distribution of −X. Because the collection {(−∞, a] : a ∈ R} generates t...

Economic Inequality, Redistribution, and Political Inequality

Based on individual and macro-level data collected in 18 OECD democracies, we find that income inequality at the macrolevel depresses electoral participation. At the level of individual citizens, we find that the effects of income differentials are linear: individuals who are below the median income in society are less likely to participate in elections, while those above the median income are ...

Improvement of Aczél’s Inequality and Popoviciu’s Inequality