In this paper we investigate the connection between the class SV s of slowly varying sequences (in the sense of Karamata) and the slow equivalence, strong asymptotic equivalence, selection principles and game theory.
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
In this paper we investigate certain connections between the class Rs,? of
rapidly varying sequences (in the sense of de Haan) and the rapid
equivalence, selection principles and game theory.
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