Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 57, Issue 4, Pages 1789-1843Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2008.57.3622
Keywords
multifractals; multifractal spectra; L-q spectra; in-homogenous self-similar measure; in-homogenous self-similar set; self-similar measure
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Let S-i : R-d -> R-d for i = 1,...,N be contracting similarities. Also, let (P-1, - - -, P-N, P) be a probability vector and let nu be a probability measure on R-d with compact support. Then there exists a unique probability measure mu on R-d such that mu = Sigma P-i(i)mu circle S-i(-1) + P nu The mesure mu is called an in-homogenous self-similar measure.
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