$BV$-packing integral in $\mathbb{R}^n$

TL;DR

This paper introduces new packing integrals in al R^n that unify and extend previous integral concepts, proving a generalized Gauss-Green theorem and comparing with existing integrals.

Contribution

It presents novel packing al integrals combining advantages of prior integrals, along with a generalized Gauss-Green theorem and comparative analysis.

Findings

Established Gauss-Green theorem for new integrals

Compared new integrals with existing ones like Pfeffer and Malfd integrals

Demonstrated the advantages of the new packing integrals

Abstract

We introduce new integrals (called packing $\mathcal{R}$ and $\mathcal{R}^*$ integrals) which combine advantages of integrals developed by Pfeffer, Mal\'y, Kuncov\'a & Mal\'y and Mal\'y & Pfeffer. We prove Gauss-Green theorem in generality of the new integrals and provide comparison with the integrals mentioned above and some others (like $MC_{\alpha}$ by Ball and Preiss).