Year: 2026
Type: preprint
Abstract: We survey several non-absolutely convergent integrals, including the Henstock-Kurzweil and Pfeffer integrals, and use ideas from these theories to investigate the problem of multidimensional Young integration. We further present results on Young geometric integration, namely the integration of certain generalized differential forms over $m$-dimensional subsets of $\mathbb{R}^d$. This is achieved by introducing appropriate notions of chains and cochains, in the spirit of Whitney's geometric integration theory.
Source: arXiv (Cornell University)
Author: Bouafia, Philippe
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128611142
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