1. Introduction

2. Hornich-Hlawka Inequality by Transfer from an $L^{1}$ Space

3. The Levy Transfer Theorem

5. The Hornich-Hlawka Inequality in Uniformly Non-Square Spaces

6. Levi’s Reduction Theorem

7. The Generalization of a Result Due to Ressel

8. The Case of Arbitrarily Large Families of Elements

9. Hornich-Hlawka Operators?

10. Further Comments