Approach to the summable ideal by O'Malley density of special testing sets on the real line

Abstract

The summable ideal for a harmonic series is described by the O'Malley density of subsets of the real line generated by sequences of reals.
Since this approach leads to a special kind of summable ideals,
we investigate the relationship between them and
we find conditions under which summable ideals
for specific series coincide with one
for the harmonic series.