In this talk I will try to describe
(part of) an ongoing reasearch with D. Preiss and M. Csoernyei.
The starting point is a decomposition
theorem for null sets (sets of measure zero) in the plane, which can be
obtained as a direct consequence of a geometric version of the Erdos-Szekeres
theorem.
I will outline some applications
to problems in Geometric Measure Theory (and not only), and if time permits,
I will finally address the issue of
extending these results to higher
dimensions.
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