On the limits of real-valued functions in sets involving ψ-density, and applications

2020/06/03 by Janne Heittokangas, Zinelaâbidine Latreuch, Heittokangas, J. +5
Mathematics · #Advanced Topology and Set Theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Primary 26A12 #Secondary 30D30

paper · pdf · doi:10.48550/arxiv.2006.02066

openalex publication_date 2020/06/03 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We prove new results on upper and lower limits of real-valued functions by means of ψ-densities introduced by P. D. Barry in 1962. This allows us to improve several existing results on the growth of non-decreasing and unbounded real-valued functions in sets of positive density. The ψ-densities are also used to introduce a new concept of a limit for real-valued functions. The results in this paper are of interest in real analysis as well as in the theory of meromorphic functions.

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