Vitali type theorems are results stating that out of a given family of sets one can select pairwisedisjoi n t sets which fill out a "large" region. Usually one works with "regular" sets such as balls. We shall establish results with sets of a more complicated geomelrical structure, e.g.. Cantor-like sets arc allowed. The results are related to a generalisation of the classical notion of a differentiation busis-They concern real n-space Ft" and Lebesgue measure.
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