Lineare Gleichverteilung

Abstract

In this paper a new concept of uniform distribution is defined which-unlike the usual definitions-does not depend on a measure-theoretical structure, but on a linear metric structure. It is shown that this concept coincides with the classical one in the s-dimensional real space. Furthermore, an explicit example shows that the concept is applicable in infinite-dimensional vector spaces: a sequence {x_k}⊂c_o is constructed which is linearly uniformly distributed.