On various definitions of density (survey).

*(English)*Zbl 1150.11339The paper provides a survey of know results about various concepts of density of subsets of \(\mathbb N\). The following densities are studied: asymptotic density, Schnirelmann density, logarithmic density, uniform density, exponential density, weighted densities. For each kind of density the author includes apart from their definitions and basic known results also several useful references.

The author roughly classifies densities into isobaric (contribution of every number to the density is the same) and weighted densities. He also discusses axioms which could be convenient in attempts to introduce an axiomatic definition of density. In the last section he briefly mentions links to other related concepts: relative density, densities on semigroups and regular matrix transformations.

The author roughly classifies densities into isobaric (contribution of every number to the density is the same) and weighted densities. He also discusses axioms which could be convenient in attempts to introduce an axiomatic definition of density. In the last section he briefly mentions links to other related concepts: relative density, densities on semigroups and regular matrix transformations.

Reviewer: Martin Sleziak (Bratislava)

##### MSC:

11B05 | Density, gaps, topology |