How projections affect the dimension spectrum of fractal measures

@inproceedings{Hunt1997HowPA,
  title={How projections affect the dimension spectrum of fractal measures},
  author={Brian R. Hunt and Vadim Kaloshin},
  year={1997}
}
We introduce a new potential-theoretic definition of the dimension spectrum Dq of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if 1< q 6 2 andμ is a Borel probability measure with compact support inR, then under almost every linear transformation from R to R, the q-dimension of the image ofμ is min(m,Dq(μ)); in particular, theq-dimension ofμ is preserved provided m > Dq(μ). We also present results on the preservation of… CONTINUE READING
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