Multifractal Measures and a Weak Separation Condition

@article{Lau1999MultifractalMA,
  title={Multifractal Measures and a Weak Separation Condition},
  author={Ka-Sing Lau and Sze-Man Ngai},
  journal={Advances in Mathematics},
  year={1999},
  volume={141},
  pages={45-96}
}
Abstract We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal formalism under such condition. 

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