Original scientific paper

On sequences of positive integers containing arithmetical progressions

T. Šalát
J. Tomanová

Abstract

We study from the metrical and topological point of view the properties of sequences of positive integers which consist in fact that the sequences contain arbitrarily long arithmetical progressions and infinite arithmetical progressions, respectively. At the end of the paper we give another solution of the problem of R. C.
Buck concerning the class $\mathcal{D}_{\mu}$ of all $A
\subseteq N$ having Buck's measure $\mu(A)$.

Keywords

density; Baire category; Lebesgue measure; Hausdorff dimension; arithmetic progression

Hrčak ID:

659

URI

https://hrcak.srce.hr/659

Publication date:

23.6.2005.

Visits: 1.920 *