Product Gauges for Product Domains

TL;DR

This paper explores the concept of gauges in the context of multi-dimensional product domains within generalized Riemann integration, aiming to extend the understanding of partition regulation in higher dimensions.

Contribution

It introduces the notion of product gauges for multi-dimensional domains, advancing the theoretical framework of gauge-based integration.

Findings

Defined product gauges for multi-dimensional domains

Extended gauge concepts to Cartesian product spaces

Provided theoretical insights into multi-dimensional integration

Abstract

In generalized Riemann integration (or Henstock-Kurzweil integration), the formation of the partitions used in Riemann sum construction is regulated by rules known as gauges. This article examines gauges for multi-dimensional Cartesian product domains.