# On the Henstock-Kurzweil Integral for Riesz-space-valued Functions on Time Scales

## TL;DR

This paper extends the Henstock-Kurzweil integral to Riesz-space-valued functions on time scales, establishing fundamental properties and convergence theorems to unify integral concepts across different mathematical contexts.

## Contribution

It introduces the HK integral for Riesz-space-valued functions on time scales, providing foundational properties and convergence results.

## Key findings

- Established basic properties of the HK delta integral for Riesz-space-valued functions.
- Proved uniform and monotone convergence theorems for the integral.
- Unified integral framework on time scales for Riesz-space-valued functions.

## Abstract

We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone convergence theorems.