Absolute equal distribution of families of finite sets. (Q1873701)

Motivated by recent results on the distribution of eigenvalues and singular values of Toeplitz matrices, two different definitions dealing with families \(U\), \(V\) of finite real sets with respect to a set \(F\) of continuous real-valued functions are considered, namely equal and absolutely equal distribution. It is shown that under certain conditions on \(F\) these definitions are equivalent. For certain function sets \(F\) sufficient conditions for \(U\), \(V\) being equally distributed are given.