Integer-valued valuations
Abstract
We obtain a complete characterization of planar monotone σ -continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity or σ -continuity and give a full classification of line valuations. We also introduce a construction of the product for valuations of this type.
Fields of Study & Subjects
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Advanced Topology and Set Theory
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 489
- Pages
- 110823–110823
- Publication date
- 29 January 2026
- Language
- EN