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arXiv · 2006.02066

On the limits of real-valued functions in sets involving $ \psi $-density, and applications

J. Heittokangas·Z. Latreuch·J. Wang·M. A. Zemirni
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Abstract

We prove new results on upper and lower limits of real-valued functions by means of $\psi$-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 $\psi$-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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J. Heittokangas, Z. Latreuch, J. Wang, M. A. Zemirni. 2020-06-03. On the limits of real-valued functions in sets involving $ \psi $-density, and applications. https://arxiv.org/abs/2006.02066

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