By Camillo De Lellis
The characterization of rectifiable units in the course of the lifestyles of densities is a pearl of geometric degree concept. The tricky facts, as a result of Preiss, will depend on many appealing and deep principles and novel options. a few of them have already confirmed worthwhile in different contexts, while others haven't but been exploited. those notes supply an easy and brief presentation of the previous and supply a few point of view of the latter. this article emerged from a direction on rectifiability given on the collage of Zurich. it truly is addressed either to researchers and scholars; the single prerequisite is a superior wisdom in usual degree idea. the 1st 4 chapters supply an creation to rectifiable units and measures in Euclidean areas, masking classical subject matters akin to the realm formulation, the concept of Marstrand and the main hassle-free rectifiability criterions. The 5th bankruptcy is devoted to a refined rectifiability criterion as a result of Marstrand and generalized by way of Mattila, and the final 3 specialise in Preiss' end result. the purpose is to supply a self-contained reference for a person attracted to an outline of this attention-grabbing subject.
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