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.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Andrea Cerri, Patrizio Frosini, Claudia Landi
• Keywords: 1-dimensional Case, CORR 2006, Education, Multidimensional Size Functions, Size Theory