# A Henstock-Kurzweil type integral on 1 dimensional integral currents

## TL;DR

This paper introduces a new non-absolutely convergent integral on 1-dimensional integral currents in Euclidean space, extending Henstock-Kurzweil integration, and proves a generalized Fundamental Theorem of Calculus for these currents.

## Contribution

It defines a novel integral on 1-dimensional currents related to Henstock-Kurzweil integrals and establishes a generalized Fundamental Theorem of Calculus for these currents.

## Key findings

- Defines a non-absolutely convergent integral on 1-dimensional integral currents.
- Proves a generalized Fundamental Theorem of Calculus for these currents.
- Provides a detailed presentation of Henstock-Kurzweil integration for accessibility.

## Abstract

We define a non-absolutely convergent integration on integral currents of dimension 1 in Euclidean space. This integral is closely related to the Henstock-Kurzweil and Pfeffer Integrals. Using it, we prove a generalized Fundamental Theorem of Calculus on these currents. A detailed presentation of Henstock-Kurzweil Integration is given in order to make the paper accessible to non-specialists.