Subsets of Rectifiable curves in Hilbert Space-The Analyst’s TSP

@inproceedings{Schul2008SubsetsOR,
  title={Subsets of Rectifiable curves in Hilbert Space-The Analyst’s TSP},
  author={Raanan Schul},
  year={2008}
}
We study one dimensional sets (Hausdorff dimension) lying i n a Hilbert space. The aim is to classify subsets of Hilbert spaces that are contained in a connected set of finite Hausdorff length. We do so by extending and improving results of Peter J ones and Kate Okikiolu for sets inRd. Their results formed the basis of quantitative rectifiabil ity in Rd. We prove a quantitative version of the following statement: a connect ed set of finite Hausdorff length (or a subset of one), is characterized… CONTINUE READING