* If <math> g </math> is a convex function defined on a real interval, then <math> \sum_{i=1}^n g(x_i) </math> is Schur-convex.
* SomeA probability examplesexample: If <math> X_1, \dots, X_n </math> are [[exchangeable random variables]], then the function <math> \text{E} \prod_{j=1}^n X_j^{a_j} </math> is Schur-convex as a function of <math> a=(a_1, \dots, a_n) </math>, assuming that the expectations exist.
:<math> \text{E} \prod_{j=1}^n X_j^{a_j} </math>
is Schur-convex as a function of <math> a=(a_1, \dots, a_n) </math>, assuming that the expectations exist.
* The [[Gini coefficient]] is strictly Schur concave.
