turkmath.org

In this talk, we will use natural density to obtain the space statistically bounded sequences (st-b-S) which is the statistical extension of the space bounded sequences (b-S). It will be shown that the space st-b-S is not only a linear space, but also a Banach space with the norm generated using density.

In the last part of the talk, we will prove that there is no matrix extension of  the spece b-S such that its bounded sequences space covers st-b-S. Finally, it is shown that the space b-S is a non porous subset of st-b-S.