Logarithmic (translationally) rapidly varying sequences and selection principles

Abstract

© 2020 Mathematical Institute of the Serbian Academy of Sciences and Arts. We introduce a proper subclass of the class of rapidly varying sequences (logarithmic (translationally) rapidly varying sequences), motivated by a notion in information theory (self-information of the system). We prove some of its basic properties. In the main result, we prove that Rothberger's and Kocinac's selection principles hold, when this class is on the second coordinate, and on the first coordinate we have the class of positive and unbounded sequences.