# Means of infinite sets I

## TL;DR

This paper explores various methods to define and analyze means on infinite sets, examining their properties and interrelations through diverse mathematical approaches.

## Contribution

It introduces multiple novel methods for defining means on infinite sets and studies their properties and relationships.

## Key findings

- Different methods for defining means on infinite sets are characterized.
- Relations between various mean definitions are established.
- Properties of these means are systematically analyzed.

## Abstract

We open a new field on how one can define means on infinite sets. We investigate many different ways on how such means can be constructed. One method is based on sequences of ideals, other deals with accumulation points, one uses isolated points, other deals with average using integral, other with limit of average on surroundings and one deals with evenly distributed samples. We study various properties of such means and their relations to each other.