Means of unbounded sets

TL;DR

This paper explores generalized means applicable to unbounded sets, examining their properties, extensions from bounded sets, and introducing new examples and generalizations of classic means.

Contribution

It introduces a framework for extending means to unbounded sets and generalizes classic means with new examples, expanding the scope of mean functions.

Findings

Extended means to unbounded sets with preserved properties

Generalized classic means for broader set classes

Presented new examples of means on unbounded sets

Abstract

We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be extended to this type of mean. We generalize some classic means and also present many new examples for means defined on unbounded sets.