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Open Access Publications from the University of California

Scholarly Works (2 results)

  • Article
  • Peer Reviewed
UC Irvine Previously Published Works (2018)
For a compact set K⊂ℝ1 and a family {Cλ}λϵJ of dynamically defined Cantor sets sufficiently close to affine with dimH K + dimH Cλ > 1 for all λ ϵ J, under natural technical conditions we prove that the sum K+C\ has positive Lebesgue measure for almost all values of the parameter λ. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than 1.
    Cover page: On sums of nearly affine Cantor sets
    • Thesis
    • Peer Reviewed
    UC Irvine Electronic Theses and Dissertations (2015)

    For a compact set K ⊂ R1 and a family {Cλ}λ∈J of dynamically defined Cantor sets sufficiently close to affine with dimH K +dimH Cλ > 1 for all λ ∈ J, we prove that the sum K+Cλ has positive Lebesgue measure for almost all values of the parameter λ. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than one.

      Cover page: Arithmetic Sums of Nearly Affine Cantor Sets
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