** separation of property with equitable distribution-in instances of inequality between spouses, an underprivileged spouse may be awarded some of the dominant spouse's property by the courts.

** Theil index, a special case of the generalized entropy index used to measure economic inequality

** Noether inequality

** Minkowski inequality

** Income inequality in the United States

** Wealth inequality in the United States

which can be proved using Jensen's inequality.

* Jensen's inequality

A combination of Hölder's inequality and Jensen's inequality implies that

( Note that this particular case of the Bernoulli distribution has the lowest possible excess kurtosis ; this can be proved by Jensen's inequality as follows.

This result, known as Jensen's inequality underlies many important inequalities ( including, for instance, the arithmetic-geometric mean inequality and Hölder's inequality ).

* Jensen's inequality

Jensen's inequality generalizes the statement that a secant line of a convex function lies above the graph.

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

Jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function, while the graph of the function is the convex function of the weighted means,

There are also converses of the Jensen's inequality, which estimate the upper bound of the integral of the convex function.

The classical form of Jensen's inequality involves several numbers and weights.

For a real convex function, numbers x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > in its domain, and positive weights a < sub > i </ sub >, Jensen's inequality can be stated as:

For instance, the function log ( x ) is concave ( note that we can use Jensen's to prove convexity or concavity, if it holds for two real numbers whose functions are taken ), so substituting in the previous formula ( 4 ) establishes the ( logarithm of ) the familiar arithmetic mean-geometric mean inequality:

Then Jensen's inequality can be applied to get

That inequality is a case of Jensen's inequality, although it may also be shown to follow instantly from the frequently mentioned fact that

For the proof of the more general version, Jensen's inequality cannot be dispensed with.

Using the Jensen's inequality on the definition of mutual information, we can show that I ( X ; Y ) is non-negative ; so consequently, H ( X ) ≥ H ( X | Y ).