Densities in disjoint unions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0956.11007
author: Georges Grekos
publication date: 2001-03-13T00:00:00Z
full work available at URL: https://eudml.org/doc/32138
Mathematics Subject Classification ID: 11B05
zbMATH DE Number: 1575486
zbMATH Keywords: density
zbMATH Keywords: sequence
zbMATH Keywords: partition
MaRDI profile type: Publication
cites work: Measure-theoretic properties of non-measurable sets
title: Densities in disjoint unions
published in: Mathematica Slovaca
review text: The author proves necesssary and sufficient conditions satisfied by the lower and upper asymptotic density of three sets \(A, B\) and \(C = A \cup B\), of positive integers. These conditions are two inequalities. Proofs are constructive, and use the properties of piecewiese linear continuous functions. In the first part of the proof three functions \(a, b, c\) are constructed. In the second part using these three functions there are constructed sets \(A,B,C\) with prescribed lower and upper asymptotic density.
reviewed by: Milan Paštéka
description: scientific article