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A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of… Click to show full abstract
A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of Moran measures and study their lower and upper local dimensions. We show that the related "free energy" function ($L^q$-spectrum) does not exist. Nevertheless, we can obtain the full Hausdroff and packing dimension spectra for level sets defined by lower and upper local dimensions. They can be viewed as a generalized multifractal formalism.
Keywords:
dimension;
without local;
local dimension;
moran measures;
multifractal spectra
Journal Title: Nonlinearity
Year Published: 2019
Link to full text (if available)
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Journal Title: Nonlinearity
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!