Stability in multidimensional Size Theory
<|reference_start|>Stability in multidimensional Size Theory: This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show that a foliation in half-planes can be given, such that the restriction of a multidimensional size function to each of these half-planes turns out to be a classical size function in two scalar variables. This leads to the definition of a new distance between multidimensional size functions, and to the proof of their stability with respect to that distance.<|reference_end|>
@article{cerri2006stability,
    title={Stability in multidimensional Size Theory},
    author={Andrea Cerri, Patrizio Frosini and Claudia Landi},
    journal={arXiv preprint arXiv:cs/0608009},
    year={2006},
    number={Universita' di Modena e Reggio Emilia, DISMI-85 june 2006},
    archivePrefix={arXiv},
    eprint={cs/0608009},
    primaryClass={cs.CG cs.CV}
}