The ordinary asymptotic
density of a set A of positive integers is ν(A) =limn→∞A(n)∕n, where A(n) is the
cardinality of the set A ∩{1,2,⋯,n}. It is known that the space of bounded
strongly Cesàro summable sequences are just those bounded sequences that
converge (in the ordinary sense) after the removal of a suitable collection of
terms, the indices of which form a set A for which ν(A) = 0. In this paper we
introduce a general concept of density and then examine the relationship,
suggested by the above observation, between these densities and the strong
convergence fields of various summability methods. These include all nonnegative
regular matrix methods as well as the famous nonmatrix method called almost
convergence.
