Measures by means, means by measures
Classical Analysis and ODEs
2023-12-06 v5
Abstract
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also study the properties and behavior of such generalized means that are obtained by a measure, and we provide some applications as well.
Cite
@article{arxiv.1706.03658,
title = {Measures by means, means by measures},
author = {Attila Losonczi},
journal= {arXiv preprint arXiv:1706.03658},
year = {2023}
}