# An approach to harmonic analysis on non-locally compact groups II: an invariant measure on groups of ordered type

## TL;DR

This paper develops a method to define a left-invariant, finitely additive measure on certain non-locally compact groups, extending previous cases and including reductive algebraic groups over higher dimensional local fields.

## Contribution

It introduces a new approach to harmonic analysis on non-locally compact groups by constructing invariant measures valued in extensions of real numbers.

## Key findings

- Defined a left-invariant, finitely additive measure on non-locally compact groups
- Unified previous special cases within this new framework
- Extended the analysis to reductive algebraic groups over higher dimensional local fields

## Abstract

We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover previously studied special cases, along with the case of reductive algebraic groups defined over higher dimensional local fields.