{
  "id": "1511.03556",
  "version": "v1",
  "published": "2015-11-11T16:23:44.000Z",
  "updated": "2015-11-11T16:23:44.000Z",
  "title": "The dimension of projections of self-affine sets and measures",
  "authors": [
    "Kenneth Falconer",
    "Tom Kempton"
  ],
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu is a Bernoulli measure on E with dim_H mu = dim_L mu, where dim_H and dim_L denote Hausdorff and Lyapunov dimensions, then the projection of mu in all but at most one direction has Hausdorff dimension min{dim_H mu,1}. We transfer this result to sets and show that many self-affine sets have projections of dimension min{dim_H E,1} in all but at most one direction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-11T16:23:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projection",
      "plane self-affine set",
      "linear parts",
      "bernoulli measure",
      "affine transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151103556F"
    }
  }
}