Integer-valued valuations

Abstract

We obtain a complete characterization of planar monotone $\ddot{I}ƒ$-continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity or $\ddot{I}ƒ$-continuity and give a full classification of line valuations. We also introduce a construction of the product for valuations of this type.

20 pages. Minor revision