turkmath.org

A density $\mu:\Gamma\to[0,1]$ is a finitely additive function defined on a field of subsets $\Gamma$ of a set $X$ where $\mu$ has the properties that subsets of null sets are null sets, the density of the space $X$ is 1 and, ‘bounded’ sets are null sets. Densities can be used to define statistical convergence and convergence in density: convergence in density implies statistical convergence, but the converse is not true in general. During this talk we will discuss convergence in density and statistical convergence for sequences and functions in general, and give a characterization of when the two definitions are equivalent.