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Stability in multidimensional Size Theory

Andrea Cerri·Patrizio Frosini·Claudia Landi
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Abstract

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.

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Andrea Cerri, Patrizio Frosini, Claudia Landi. 2006-08-02. Stability in multidimensional Size Theory. https://arxiv.org/abs/cs/0608009

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