Direct and inverse limits of normed modules

TL;DR

This paper investigates the existence and properties of direct and inverse limits within the category of normed L^0-modules over metric measure spaces, extending the theoretical framework of Gigli.

Contribution

It provides foundational results on the existence and characteristics of limits in the category of normed L^0-modules, a topic not extensively explored before.

Findings

Established conditions for the existence of direct and inverse limits.

Characterized main properties of these limits in the category.

Extended the theoretical framework of normed L^0-modules.

Abstract

The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.