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arXiv · 2502.21144

Integer-valued valuations

Andrii Ilienko·Ilya Molchanov·Tommaso Visonà
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Abstract

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

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Andrii Ilienko, Ilya Molchanov, Tommaso Visonà. 2025-02-28. Integer-valued valuations. https://arxiv.org/abs/2502.21144

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