On some random thin sets of integers

Mathematica Slovaca, 1997

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2002

The paper describes ergodic (with respect to the Haar measure) functions in the class of all functions, which are defined on (and take values in) the ring of p-adic integers, and which satisfy (at least, locally) Lipschitz condition with coefficient 1. Equiprobable (in particular, measure-preserving) functions of this class are described also. In some cases (and especially for p=2) the

1993

2021

A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some drawback of statistical convergence. While developing the theory of very thin sets, concepts of super thin, very very thin and super super thin sets are evolved spontaneously.

Cornell University - arXiv, 2017

Journal für die reine und angewandte Mathematik (Crelles Journal), 2000

Proceedings of the American Mathematical Society, 1997

We introduce the notion of perfectly measure zero sets and prove that every perfectly measure zero set is permitted for the families of all pseudo-Dirichlet sets, N 0-sets, A-sets and N-sets. In particular this means that these families of trigonometric thin sets are closed under adding sets of cardinality less than the additivity of Lebesgue measure.

Nieuw Archief voor Wiskunde, 1995

arXiv:1502.02601 [stat.ME], 2015

A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived

International Journal of Mathematics and Mathematical Sciences, 2003

For each integern≥2, letP(n)denote its largest prime factor. LetS:={n≥2:ndoes not divideP(n)!}andS(x):=#{n≤x:n∈S}. Erdős (1991) conjectured thatSis a set of zero density. This was proved by Kastanas (1994) who established thatS(x)=O(x/logx). Recently, Akbik (1999) proved thatS(x)=O(x exp{−(1/4)logx}). In this paper, we show thatS(x)=x exp{−(2+o(1))×log x log log x}. We also investigate small and large gaps among the elements ofSand state some conjectures.